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non-trivial divisors. There are divisibility rules that allow one to recognize certain divisors of a number from the number's digits. 7 is a divisor of 42 because...

number theory, a divisor function is an arithmetic function related to the divisors of an integer. When referred to as the divisor function, it counts...

positive common divisor in the preorder relation of divisibility. This means that the common divisors of a and b are exactly the divisors of their GCD....

ring of n × n matrices over a field has nonzero zero divisors if n ≥ 2. Examples of zero divisors in the ring of 2 × 2 matrices (over any nonzero ring)...

the sum of the prices of all thirty stocks divided by a divisor, the Dow Divisor. The divisor is adjusted in case of stock splits, spinoffs or similar...

and is an element of the group of Weil divisors on X {\displaystyle X} . Consideration of exceptional divisors is crucial in birational geometry: an elementary...

called the elementary divisors. Note that in a PID, the nonzero primary ideals are powers of prime ideals, so the elementary divisors can be written as powers...

divisors are a generalization of codimension-1 subvarieties of algebraic varieties. Two different generalizations are in common use, Cartier divisors...

a positive integer that has more divisors than all smaller positive integers. If d(n) denotes the number of divisors of a positive integer n, then a positive...

list positive divisors. d(n) is the number of the positive divisors of n, including 1 and n itself σ(n) is the sum of the positive divisors of n, including...

these D do not move in a linear system of divisors on C, in the sense that they do not dominate the polar divisor of a non constant function. Riemann further...

the divisor function, denotes the number of divisors of n. The term was coined by Ramanujan (1915). For example, the number with the most divisors per...

harmonic divisor number or Ore number is a positive integer whose divisors have a harmonic mean that is an integer. The first few harmonic divisor numbers...

the unitary divisors of n is odd if n is a power of 2 (including 1), and even otherwise. Both the count and the sum of the unitary divisors of n are multiplicative...

particularly ring theory, maximal common divisors are an abstraction of the number theory concept of greatest common divisor (GCD). This definition is slightly...

divisors of 12, 16, is greater than 12. It is also the 3rd colossally abundant number. 12 is a semiperfect number because some of its proper divisors;...

term "divisorial" refers to the fact that "the topology of these varieties is determined by their positive divisors." The class of divisorial schemes...

the sum of its positive proper divisors, that is, divisors excluding the number itself. For instance, 6 has proper divisors 1, 2, and 3, and 1 + 2 + 3 =...

it is the sum of its unitary divisors excluding itself, and because it is equal to the sum of a subset of its divisors, it is also the twenty-first semiperfect...

counting the number of divisors. All composite numbers have at least three divisors. In the case of squares of primes, those divisors are { 1 , p , p 2 }...

The lowest common divisor is a term mistakenly used to refer to: Lowest common denominator, the lowest common multiple of the denominators of a set of...

combinatorial commutative algebra, a zero-divisor graph is an undirected graph representing the zero divisors of a commutative ring. It has elements of...

relative effective Cartier divisor is roughly a family of effective Cartier divisors. Precisely, an effective Cartier divisor in a scheme X over a ring...

of its positive proper unitary divisors, not including the number itself. (A divisor d of a number n is a unitary divisor if d and n/d share no common factors...

every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle 2^{d}-2} . For example, 341 is a super-Poulet number: it has positive divisors (1, 11...

15). These two numbers are the only numbers whose arithmetic mean of divisors is the first perfect number and unitary perfect number, 6 (that is also...

the numbers with exactly two positive divisors. Those two are 1 and the number itself. As 1 has only one divisor, itself, it is not prime by this definition...

(disambiguation) 203 is a number whose average of divisors is 60, the smallest number with twelve divisors and forty-second composite. On the other hand,...

smallest number with exactly 17 divisors (but there are smaller numbers with more than 17 divisors; e.g., 180 has 18 divisors) (sequence A005179 in the OEIS)...

A081357 (Sublime numbers, numbers for which the number of divisors and the sum of the divisors are both perfect.)". The On-Line Encyclopedia of Integer...

since the sum of its proper divisors, 156, is greater than 96. 96 has 12 divisors. As no smaller number has 12 or more divisors, 96 is a largely composite...

seventh tetrahedral number. The number of divisors of 84 is 12. As no smaller number has more than 12 divisors, 84 is a largely composite number. A hepteract...

terminology by making an exception for zero divisors: one calls an element a in a commutative ring a zero divisor if there exists a nonzero x such that ax...

to the sum of the proper divisors of 9: 1 + 3 = 4. The number 5 is untouchable, as it is not the sum of the proper divisors of any positive integer: 5 = 1 + 4...

The D'Hondt method, also called the Jefferson method or the greatest divisors method, is an apportionment method for allocating seats in parliaments among...

A divisor is the second operand of a division. A divisor may also refer to Divisor (number theory), an integer that divides evenly another integer Divisor...

of the Euclidean algorithm, one for right divisors and one for left divisors. Choosing the right divisors, the first step in finding the gcd(α, β) by...

semiprimes with four divisors each, where 34 is the smallest number to be surrounded by numbers with the same number of divisors it has. This is the first...

seconds? Look at the list of its twelve divisors ... Compare this with the larger number 100, which has only nine divisors." "Why is a minute divided into 60...

namely the basic open set S x {\displaystyle S_{x}} of divisors of x {\displaystyle x} . So the divisor topology is an Alexandrov topology. X {\displaystyle...

(Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer.)". The...

proper divisors of each is equal to the other number. That is, s(a)=b and s(b)=a, where s(n)=σ(n) − n is equal to the sum of positive divisors of n except...

exactly nine positive divisors, and 9 is one of them; in fact, it is the smallest positive integer with at least nine divisors, which leads 36 to be the...

of its proper divisors, the numbers that are less than it and divide it evenly (with remainder zero). For instance, the proper divisors of 6 are 1, 2...

 has no primitive prime divisors } . {\displaystyle {\mathcal {Z}}(a_{n})=\{n\geq 1:a_{n}{\text{ has no primitive prime divisors}}\}.} i.e., the set of...

000,000,000 has a total of 169 divisors (156 even, 13 odd), whose geometric mean is 1,000,000. The sum of all its divisors (including itself) is 2,499,694...

the notion of 'divisor' is inherently ambiguous (Cartier divisors, Weil divisors: see divisor (algebraic geometry)). The definition in that case is usually...

expressed as a sum of some of its divisors, making it a semiperfect number. The geometric mean of its nine divisors is 10. 100 is the sum of the cubes...

divisors of n {\displaystyle n} . For example, 12 is a practical number because all the numbers from 1 to 11 can be expressed as sums of its divisors...

whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because: The sum of its proper divisors is 1 + 2 + 4 +...

proper divisors yet equal to the sum of a subset of its proper divisors. It is a practical number as each smaller number is the sum of distinct divisors of...

k/2 for an odd integer k, where σ(n) is the sum-of-divisors function, the sum of all positive divisors of n. The first few hemiperfect numbers are: 2, 24...

h_{n}} divisors. Proof. r n − 1 = ( p 2 q ) n − 1 = p 2 ( n − 1 ) q n − 1 {\displaystyle r^{n-1}=(p^{2}q)^{n-1}=p^{2(n-1)}q^{n-1}} has divisors of the...

composite number. It is also the first number that is the sum of its proper divisors, making it the smallest perfect number. It is also the only perfect number...

which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number: its proper divisors are 1, 2, 3, 4 and 6, and...

\sigma _{k}} denotes a divisor function with σ k ( n ) {\displaystyle \sigma _{k}(n)} equal to the sum of the k-th powers of the divisors of n. The numbers...

special divisors is a result of William K. Clifford (1878) on algebraic curves, showing the constraints on special linear systems on a curve C. A divisor on...

_{k}={\text{Id}}_{k}*1} , the kth-power-of-divisors sum function σk. σ = Id ∗ 1 {\displaystyle \sigma ={\text{Id}}*1} , the sum-of-divisors function σ = σ1. τ = 1 ∗ 1...

smallest number with exactly 11 divisors (but there are smaller numbers with more than 11 divisors; e.g., 60 has 12 divisors) (sequence A005179 in the OEIS)...

Myzostoma divisor is a species of parasitic marine polychaete in the order Myzostomida. M. divisor is a free-living, ectocommensal parasite of various...

is never a domain: if R is nonzero, such a matrix ring has nonzero zero divisors and even nilpotent elements other than 0. For example, the square of the...

A054979 (e-perfect numbers: numbers k such that the sum of the e-divisors (exponential divisors) of k equals 2*k.)". The On-Line Encyclopedia of Integer Sequences...

bundles to divisors, the first Chern class is the isomorphism from the Picard group of line bundles on a variety X to the group of Cartier divisors modulo...

particular, rigorous sense, has many divisors. Particularly, it is defined by a ratio between the sum of an integer's divisors and that integer raised to a power...

in the divisor. For instance, one cannot make a rule for 14 that involves multiplying the equation by 7. This is not an issue for prime divisors because...

the sum of all or some of its proper divisors. A semiperfect number equal to the sum of all its proper divisors is a perfect number. The first few semiperfect...

Laphria divisor is a species of robber flies in the family Asilidae. "Laphria divisor Report". Integrated Taxonomic Information System. Retrieved 2018-04-20...

multiplicative inverses, but they are not a division algebra because they have zero divisors: two nonzero sedenions can be multiplied to obtain zero, for example ⁠...

OEIS: A103432. Norm 1–250 251–500 501–750 751–1000 Gaussian integer Table of divisors Integer factorization Dresden, Greg; Dymacek, Wayne (2005). "Finding factors...

decimal since the sum of its digits (9) is a divisor of 360. 360 is divisible by the number of its divisors (24), and it is the smallest number divisible...

In number theory, the divisor summatory function is a function that is a sum over the divisor function. It frequently occurs in the study of the asymptotic...

between line bundles and divisors (built from codimension-1 subvarieties), there is an equivalent notion of an ample divisor. In more detail, a line bundle...

the sum of its proper divisors (66), is greater than itself. Like all multiples of 6, 54 is equal to some of its proper divisors summed together, so it...

Cardinal one Ordinal 1st (first) Numeral system unary Factorization ∅ Divisors 1 Greek numeral Α´ Roman numeral I, i Greek prefix mono-/haplo- Latin prefix...

divisors. Together with the Jacobi inversion problem, we can say that J ( M ) {\displaystyle J(M)} is isomorphic as a group to the group of divisors of...

Cardinal ten Ordinal 10th (tenth) Numeral system decimal Factorization 10 Divisors 1, 2, 5, 10 Greek numeral Ι´ Roman numeral X, x Roman numeral (unicode)...

In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane. Heegner points...

8 + 8 = 80. A semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20, and 40) gives 80. A ménage number. Palindromic...

of the proper divisors (divisors including 1 but not itself) of the number is greater than the number, but no subset of those divisors sums to the number...

three consecutive integers: 99 = 23 + 33 + 43. the sum of the sums of the divisors of the first 11 positive integers. 99 70 = 1.4142 8571 … {\displaystyle...

What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division...

number, with its proper divisors summing up to 366. 180 is also the 11th highly composite number, a positive integer with 18 divisors, more than any smaller...

number that is a perfect cube. Sphenic numbers always have exactly eight divisors. 8 is the base of the octal number system. A polygon with eight sides is...

142. 141 is: a centered pentagonal number. the sum of the sums of the divisors of the first 13 positive integers. the second n to give a prime Cullen...

N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia...

F(2) = 1, which have no prime divisors F(6) = 8, whose only prime divisor is 2 (which is F(3)) F(12) = 144, whose only prime divisors are 2 (which is F(3)) and...

called divisors. The earliest work on algebraic cycles focused on the case of divisors, particularly divisors on algebraic curves. Divisors on algebraic...

{\displaystyle z} is called a "left" topological divisor of zero, and one may define "right" topological divisors of zero similarly. If A {\displaystyle A} has...

following 219 and preceding 221 It is a composite number, with its proper divisors being 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110, making it an amicable...

special divisors, certain divisors on a curve C that determine more compatible functions than would be predicted. In classical language, special divisors move...

its proper divisors (which excludes itself) is less than itself. As an integer for which the arithmetic mean average of its positive divisors is also an...

composite de Polignac number. 1208 = 23 × 151. There are 1208 strict chains of divisors starting with the superprimorial A006939(3). 1210 = 2 × 5 × 112. It is...

at least 3), Riemann-Roch, and the theory of special divisors is rather close. Effective divisors D on C consisting of distinct points have a linear span...

integer n for which the sum of divisors of n is less than 2n. Equivalently, it is a number for which the sum of proper divisors (or aliquot sum) is less than...

average of its positive divisors is also an integer. For instance, 6 is an arithmetic number because the average of its divisors is 1 + 2 + 3 + 6 4 = 3...

smallest: −2, −1, 0, 1, 4, 5, 9, 56, and 636. The divisors of negative two, including negative divisors, are identical to those of two: −2, −1, 1, 2. By...

instead of Hayes. The two names for these methods—highest averages and divisors—reflect two different ways of thinking about them, and their two independent...

equivalence classes of divisors on V; that is, using a stronger, non-linear equivalence relation in place of linear equivalence of divisors, the classification...

11012 – via Taylor & Francis. Sloane, N. J. A. (ed.). "Sequence A222262 (Divisors of Descarte's 198585576189.)". The On-Line Encyclopedia of Integer Sequences...

first four primes (87 = 22 + 32 + 52 + 72). the sum of the sums of the divisors of the first 10 positive integers. the thirtieth semiprime, and the twenty-sixth...

Cono (literally: "Cone Hill") is a mountain located in the Sierra del Divisor National Park in the Ucayali Department of Peru. The mountain has never...

relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides a does...

number of divisors can be computed by increasing all multiplicities by 1 and then multiplying them. Divisors and properties related to divisors are shown...

number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that τ ( n ) ∣ n {\displaystyle...

sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. The aliquot...

or simply 1E13 in E notation). It has a total of 196 divisors (182 even, 14 odd). All divisors are displayed below: 1, 2, 4, 5, 8, 10, 16, 20, 25, 32...

and broadest of the "Bertini theorems" applying to a linear system of divisors; simplest because there is no restriction on the characteristic of the...

called k-perfect (or k-fold perfect) if the sum of all positive divisors of n (the divisor function, σ(n)) is equal to kn; a number is thus perfect if and...

Sierra del Divisor is a mountain range located in the border between Peru and Brazil, rising up from the Amazonian plain. It is the only mountainous area...

equivalence classes of divisors on V; that is, using a stronger, non-linear equivalence relation in place of linear equivalence of divisors, the classification...

divisors which have a finite or terminating decimal expansion (i.e. decimal fractions). In this case the procedure involves multiplying the divisor and...

also the smallest primitive abundant number because all of its proper divisors are deficient. The Happy Family of sporadic groups is made up of twenty...

useful identities related to number-theoretic divisor sums, i.e., sums of an arithmetic function over the divisors of a natural number n {\displaystyle n} ...

sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, s ( n ) = ∑ d | n , d...

and preceding 29. 28 is a composite number, a perfect number, a harmonic divisor number, a centered nonagonal number, a hexagonal number, a happy number...

Trial division is the most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests...

number with the property that the sum of its divisors (including itself) is greater than the sum of the divisors of any smaller natural number. Highly abundant...

because 52 is an untouchable number, meaning it is never the sum of proper divisors of any number. It is the first untouchable number larger than 2 and 5....

satisfies the problem's statement. A brute-force algorithm that finds the divisors of a natural number n would enumerate all integers from 1 to n, and check...

A005835 (Pseudoperfect (or semiperfect) numbers n: some subset of the proper divisors of n sums to n.)". The On-Line Encyclopedia of Integer Sequences. OEIS...

natural number after 271 and before 273. 272 is a composite number, with divisors 1, 2, 4, 8, 16, 17, 34, 68, 136, and 272. It can be expressed as the sum...

nontrivial decimal reverse divisor must be either 1/4 or 1/9 of its reversal. The number of d-digit nontrivial reverse divisors is 2 F ( ⌊ ( d − 2 ) / 2...

natural number following 114 and preceding 116. 115 has a square sum of divisors: σ ( 115 ) = 1 + 5 + 23 + 115 = 144 = 12 2 . {\displaystyle \sigma...

2 k {\displaystyle n=2^{k}} divisors is the product of the k {\displaystyle k} smallest Fermi–Dirac primes. Its divisors are the numbers obtained by multiplying...

greatest common divisor. The theorem's statement is as follows: Bézout's identity—Let a and b be integers with greatest common divisor d. Then there exist...

Ordinal 7th (seventh) Numeral system septenary Factorization prime Prime 4th Divisors 1, 7 Greek numeral Ζ´ Roman numeral VII, vii Greek prefix hepta-/hept-...

possible divisors up to n {\displaystyle n} are tested, some divisors will be discovered twice. To observe this, consider the list of divisor pairs of...

in 1918. In a sociable sequence, each number is the sum of the proper divisors of the preceding number, i.e., the sum excludes the preceding number itself...

The square-free part of n {\displaystyle n} is the product of all prime divisors of n {\displaystyle n} whose exponent in the factorization of n {\displaystyle...

myriad to the power of itself, 1000010000 = 1040000. It has a total of 25 divisors, whose geometric mean is a whole number, 100 (the number of primes below...

number of positive divisors, while other natural numbers have an even number of positive divisors. An integer root is the only divisor that pairs up with...

(f)} is a divisor of degree 0. Such divisors, i.e. divisors coming from some rational function f {\displaystyle f} , are called principal divisors and the...

numbers. The canonical representations of the product, greatest common divisor (GCD), and least common multiple (LCM) of two numbers a and b can be expressed...

(Weil) divisor. The Cartier divisors form a subgroup of the group of divisors containing the principal divisors. The quotient of the Cartier divisors by the...

Integer-valued polynomials may be used effectively to solve questions about fixed divisors of polynomials. For example, the polynomials P with integer coefficients...

same divisors, the set of the common divisors is not changed by Euclid's algorithm and thus all pairs (ri, ri+1) have the same set of common divisors. The...

(30). However, there is no integer that has 120 as the sum of its proper divisors, making 120 an untouchable number. The sum of Euler's totient function...

multiples of 2, 945 has 3, 5 and 7 as divisors, and 88 is the first abundant number that doesn't have 3, 5 or 7 as divisors. 88 symbolizes fortune and good...

prime factorization 2 3 ⋅ 7 {\displaystyle 2^{3}\cdot 7} . Its proper divisors are 1, 2, 4, 7, 8, 14, and 28, whose sum is 64, so 56 is an abundant number...

divisors than any smaller odd numbers. After 1 and 9, 225 is the third smallest number n for which σ(φ(n)) = φ(σ(n)), where σ is the sum of divisors function...

integer to start a run of four consecutive integers with the same number of divisors. R. K. Guy Unsolved Problems in Number Theory, section B18. D. Wells, The...

set up divisor (13) for second division loop (MEMORY LAYOUT: zero copy dividend divisor remainder quotient zero zero) >-[>+>>] Reduce divisor; Normal...

eight times the sum of the divisors of n if n is odd and 24 times the sum of the odd divisors of n if n is even (see divisor function), i.e. r 4 ( n )...

harmonic divisor number. Another consequence of 8128 being a perfect number is that it has the same prime factors as the sum of its divisors, and its...

and are 2 away from another prime number. 282 is equal to the sum of its divisors containing the number 4. It is the sum of 47 + 94 + 141. 282 is the number...

rank-index methods are a set of apportionment methods that generalize the divisor method. These have also been called Huntington methods, since they generalize...

2016-05-30. Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS...

preceding 275. 274 is an even composite number. 274's sum of its proper divisors is 140. The number 274 is the 13th tribonacci number. This is defined by...

perform the algorithm; this algorithm includes steps for dividing non-monic divisors: Write the coefficients of the dividend on a bar.   a 7 a 6 a 5 a 4 a 3...

by the number of divisors it has, 12, making it a refactorable number. 108 is a largely composite number because it has 12 divisors and no smaller number...

divisible: 360 has 24 divisors, making it one of only 7 numbers such that no number less than twice as much has more divisors (sequence A02182 in the...

first three Mersenne primes, 3, 7, 31. It is the sum of the sum of the divisors of the first 7 positive integers. It is the sum of two consecutive squares...

technique he found that 1166 out of the first three million primes are divisors of Sylvester numbers, and that none of these primes has a square that divides...

generated base field. The Tate conjecture for divisors on abelian varieties implies the Tate conjecture for divisors on any product of curves C 1 × ⋯ × C n {\displaystyle...

prime number (or prime) is a natural number greater than 1 that has no divisors other than 1 and itself. By Euclid's theorem, there are an infinite number...

n}{\overline {Q}}_{n}(E,F),} where the products are taken over all divisors of n, or all divisors of 2n that do not divide n, and Q n ( x ) {\displaystyle Q_{n}(x)}...

(the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental...

prime of the form p4: 16 = 24. It is the smallest number with exactly five divisors: 1, 2, 4, 8, and 16. Sixteen is the only integer that equals mn and nm...

they are the numbers whose only prime divisors are 2, 3, and 5. As an example, 602 = 3600 = 48 × 75, so as divisors of a power of 60 both 48 and 75 are...

{\displaystyle \varphi (n)} of 72 is equal to the totient value of its sum-of-divisors: φ ( 111 ) = φ ( σ ( 111 ) ) . {\displaystyle \varphi (111)=\varphi (\sigma...

633-hectare (2,092,080-acre) Serra do Divisor National Park, created in 1989. IBGE 2020 PARNA da Serra do Divisor (in Portuguese), ISA: Instituto Socioambiental...

{2, 1}. The divisor function τ(n), the Möbius function μ(n), the number of distinct prime divisors ω(n) of n, the number of prime divisors Ω(n) of n, the...

N. J. A. (ed.). "Sequence A001065 (Sum of proper divisors (or aliquot parts) of n: sum of divisors of n that are less than n.)". The On-Line Encyclopedia...

Cardinal four Ordinal 4th (fourth) Numeral system quaternary Factorization 22 Divisors 1, 2, 4 Greek numeral Δ´ Roman numeral IV (subtractive notation) IIII (additive...

the sense of category theory) way to turn a subvariety into a Cartier divisor. A blowup can also be called monoidal transformation, locally quadratic...

commutative rings R that may have zero divisors. The construction embeds R in a larger ring, giving every non-zero-divisor of R an inverse in the larger ring...

the Hall divisors of 60, its prime power factorization is 22 × 3 × 5, so one takes any product of 3, 22 = 4, and 5. Thus, the Hall divisors of 60 are...

A and B, the divisors are to be adjusted. The divisor for A has to be raised and the divisor for B has to be lowered: Now, the divisors for regions I...

semiprime and the first odd and fourth discrete semiprime. Its proper divisors are 1, 3, and 5, so it is the first semiprime of the form 3 × q, where...

Erdős on the intersection of the Euler Totient function and the sum of divisors function. Luca was born in Galați and graduated with a BS in Mathematics...

It is a balanced number It is the 15th highly composite number, with 32 divisors: 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42...

following 139 and preceding 141. 140 is an abundant number and a harmonic divisor number. It is the sum of the squares of the first seven integers, which...

digits. 268 is untouchable which means that it is not the sum of the proper divisors of any number 268 is the sum of the consecutive primes 131 and 137. "Facts...

The Serra do Divisor National Park (Portuguese: Parque Nacional da Serra do Divisor) is a 8,463 km2 (3,268 mi2) national park on the westernmost point...

19 {\displaystyle 3\cdot 19} , and is therefore a semiprime. Its proper divisors are 1, 3, and 19, whose sum is 23, so 57 is a deficient number. Since both...

{1}{N}}+\sum _{p\,|\;\!N}{\frac {1}{p}}=1,} where the sum is over only the prime divisors of N. Equivalently, N is a primary pseudoperfect number if it satisfies...

6174th (six thousand one hundred seventy-fourth) Factorization 2 × 32 × 73 Divisors 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 49, 63, 98, 126, 147, 294, 343, 441,...

22 · 33, and thus its prime factors are 2 and 3. Both 22 = 4 and 32 = 9 are divisors of 108. However, 108 cannot be represented as mk, where m and k are positive...

have at most three other pandigital numbers as divisors. The smallest prime number that is not a divisor of any pandigital number is 111,119. However,...

concept of a maximal common divisor is needed to generalize greatest common divisors to number systems in which the common divisors of a set of elements may...

Any divisor of this form is called a principal divisor. Two divisors that differ by a principal divisor are called linearly equivalent. The divisor of...

in analysis. divisor A divisor or factor of an integer n is an integer m such that there exists an integer k satisfying n = mk. Divisors can be defined...

Juruá River. The Môa River flows through the northern part of the Serra do Divisor National Park, and forms part of its north eastern boundary. It continues...

1-automorphic number 1,808,141,741 : number of partitions of 280 into divisors of 280 1,808,676,326 : number of 38-bead necklaces (turning over is allowed)...

quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function σ ( n ) {\displaystyle \sigma (n)} ) is equal to 2...

coordinates. The number 60, a superior highly composite number, has twelve divisors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and...

{\displaystyle \mathbb {O} } , and holds a compact form homeomorphic to the zero divisors with entries of unit norm in the sedenions, S {\displaystyle \mathbb {S}...

the multiplication property of zero, the nonexistence of nonzero zero divisors, or one of the two zero-factor properties. All of the number systems studied...

Euclidean algorithm, and computes, in addition to the greatest common divisor (gcd) of integers a and b, also the coefficients of Bézout's identity,...

seventy-five Ordinal 275th (two hundred seventy-fifth) Factorization 52 × 11 Divisors 1, 5, 11, 25, 55, 275 Greek numeral ΣΟΕ´ Roman numeral CCLXXV, cclxxv Binary...

contain zero divisors and are thus not a division algebra. Whereas the sedenions have 84 zero divisors, the trigintaduonions have 1,260 zero divisors derived...

powers of the positive divisors of n, including 1 and n, where k is a complex number. σ1(n), the sum of the (positive) divisors of n, is usually denoted...

exactly eight divisors. If we express the sphenic number as n = p  ×  q  ×  r, where p, q, and r are distinct primes, then the set of divisors of n will be:...

{Index~value} &={\frac {\mathrm {Total~market~value} }{\mathrm {Index~divisor} }}\end{aligned}} expanded to, I n d e x   v a l u e = ∑ i = 1 n ( P r...

the number of prime knots with 10 crossings. the sum of the sums of the divisors of the first 14 positive integers. a self number in base 10. a palindromic...

ninety-three Ordinal 293rd (two hundred ninety-third) Factorization prime Divisors 1, 293 Greek numeral ΣϞΓ´ Roman numeral CCXCIII, ccxciii Binary 1001001012...

of 240 into divisors of 240 28,088,787,314 = number of signed trees with 19 nodes 28,843,094,837 = number of partitions of 300 into divisors of 300 31,381...

common divisor (although it may not be possible to find it using the Euclidean algorithm). If x and y are elements of a PID without common divisors, then...

under addition on J (see theta-divisor) have dimension n and fill up J, with some identifications caused by special divisors. For g = n we have ΣgC actually...

divisor along which one allows mild logarithmic singularities. They were studied by Iitaka (1976). A boundary Q-divisor on a variety is a Q-divisor D...

number, a number with more divisors than any smaller number. If σ ( n ) {\displaystyle \sigma (n)} is the sum-of-divisors function and γ {\displaystyle...

sixty-seven Ordinal 67th (sixty-seventh) Factorization prime Prime 19th Divisors 1, 67 Greek numeral ΞΖ´ Roman numeral LXVII, lxvii Binary 10000112 Ternary...

their positive proper divisors, which are divisors excluding the number itself. So, 6 is a perfect number because the proper divisors of 6 are 1, 2, and...

of divisors of n {\displaystyle n} as d ( n ) {\displaystyle d(n)} , and write d a ( n ) {\displaystyle d_{a}(n)} for the number of those divisors with...

Having only 2 and 3 as its prime divisors, 162 is a 3-smooth number. 162 is also an abundant number, since its sum of divisors 1 + 2 + 3 + 6 + 9 + 18 + 27...

K(b^{n})} . It was shown in 2000 that there is a bijection between the unitary divisors of N − 1 {\displaystyle N-1} and the set K ( N ) {\displaystyle K(N)} defined...

previous 52 weeks is divided by the number of tournaments played (a minimum divisor of 11 is used) to give a ranking average. Where a player has played more...

cyclotomic polynomials Φ d ( x ) {\displaystyle \Phi _{d}(x)} for the proper divisors d dividing n, starting from Φ 1 ( x ) = x − 1 {\displaystyle \Phi _{1}(x)=x-1}...

If N has s distinct prime divisors, there are 2s Hall divisors of N; for example, if N = 360 = 23⋅32⋅51, the 8 Hall divisors of N are 1, 23, 32, 51, 23⋅32...

prime. It is a repdigit in quaternary (1114). As a semiprime with proper divisors 1, 3 and 7, twenty-one has a prime aliquot sum of 11 within an aliquot...

common divisor (gcd) of two Gaussian integers a, b is a Gaussian integer d that is a common divisor of a and b, which has all common divisors of a and...

more divisors than any number less than double itself (sequence A072938 in the OEIS). Not only it is the 7th (and last) number with more divisors than...

polynomials: starting from two polynomials A (the dividend) and B (the divisor) produces, if B is not zero, a quotient Q and a remainder R such that A...

→ Cardinal fifty-five Ordinal 55th (fifty-fifth) Factorization 5 × 11 Divisors 1, 5, 11, 55 Greek numeral ΝΕ´ Roman numeral LV, lv Binary 1101112 Ternary...

rings, which is why the assumption of the ring having no nonzero zero divisors is commonly made in the definition of irreducible elements. It results...

without left or right nonzero zero divisors Integral domain, a non-trivial commutative ring without nonzero zero divisors Atomic domain, an integral domain...

is isomorphic to the dual of the lattice of divisors of n, with a subgroup of order n/d for each divisor d. The subgroup of order n/d is a subgroup of...

least common divisor is a confusion of the following two distinct concepts in arithmetic: Least common multiple Greatest common divisor This disambiguation...

natural number following 260 and preceding 262. There are six divisors of this number, the divisors being 1, 3, 9, 29, 87, and 261 itself. 261 is a deficient...

positive integer with a positive divisor other than one or itself 182 is a deficient number, as the sum of its proper divisors, 154, is less than 182 182 is...

called divisorial. In other words, a divisorial ideal is a nonzero intersection of some nonempty set of fractional principal ideals. If I is divisorial and...

left nor a right zero divisor) that annihilates m, i.e., r m = 0. In an integral domain (a commutative ring without zero divisors), every non-zero element...

{\displaystyle D_{n}} are characterized entirely by the divisors of n {\displaystyle n} and each divisor has probability 1 / τ ( n ) {\displaystyle 1/\tau (n)}...

which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words,...

functions. ω ( n ) {\displaystyle \omega (n)} is the number of distinct prime divisors of n {\displaystyle n} , and Ω ( n ) {\displaystyle \Omega (n)} is the...

theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many prime numbers, and the...

product of the primitive parts. As the computation of greatest common divisors is generally much easier than polynomial factorization, the first step...

alternate choosing positive divisors of the initial number, but may not choose 1 or a multiple of a previously chosen divisor. This game models n-dimensional...

correctness is unknown as of 2023 // return the sum of proper divisors of n static int divisorSum(int n) { int i, sum = 0; for (i=1; i<n; ++i) if (n % i ==...

{\displaystyle 1111111=(1+1)^{111}-1\,} . 127 is the sum of the sums of the divisors of the first twelve positive integers. 127 is the smallest prime that can...

(Harmonic or Ore numbers: numbers k such that the harmonic mean of the divisors of k is an integer.)". The On-Line Encyclopedia of Integer Sequences. OEIS...

→ Cardinal eighty-six Ordinal 86th (eighty-sixth) Factorization 2 × 43 Divisors 1, 2, 43, 86 Greek numeral ΠϚ´ Roman numeral LXXXVI, lxxxvi Binary 10101102...

general division). For example, when dividing 20 (the dividend) by 3 (the divisor), the quotient is 6 (with a remainder of 2) in the first sense and 6 +...

cannot result in 292. 292 is an untouchable number meaning that the proper divisors of any number do not add up to 292. 292 is a repdigit in base 8 with it...

→ Cardinal twenty-six Ordinal 26th (twenty-sixth) Factorization 2 × 13 Divisors 1, 2, 13, 26 Greek numeral ΚϚ´ Roman numeral XXVI, xxvi Binary 110102 Ternary...

average number of divisors of the numbers in a range from 1 to n {\displaystyle n} , formalized as the average order of the divisor function, 1 n ∑ i...

adapted to the larger divisors as well. As in all division problems, a number called the dividend is divided by another, called the divisor. The answer to the...

90 → Cardinal twenty-five Ordinal 25th (twenty-fifth) Factorization 52 Divisors 1, 5, 25 Greek numeral ΚΕ´ Roman numeral XXV, xxv Binary 110012 Ternary...

for each integer i between 0 and k, at least one of the greatest common divisors gcd(a, a + i) or gcd(a + i, a + k) is greater than 1. 16 is an Erdős–Woods...

Cardinal thirty-three Ordinal 33rd (thirty-third) Factorization 3 × 11 Divisors 1, 3, 11, 33 Greek numeral ΛΓ´ Roman numeral XXXIII, xxxiii Binary 1000012...

common divisor (GCD) of two numbers. It is intended to demonstrate the declarative nature of Gödel, not to be particularly efficient. The CommonDivisor predicate...

preceding 133. It is 11 dozens. 132 is the sixth Catalan number. With twelve divisors total where 12 is one of them, 132 is the 20th refactorable number, preceding...

the natural number following 269 and preceding 271. 270 is a harmonic divisor number. 270 degrees is equal to three-fourths of a turn. This also means...

hundred eighteen Ordinal 118th (one hundred eighteenth) Factorization 2 × 59 Divisors 1, 2, 59, 118 Greek numeral ΡΙΗ´ Roman numeral CXVIII, cxviii Binary 11101102...

22nd (twenty-second) Numeral system Duovigesimal Factorization 2 × 11 Divisors 1, 2, 11, 22 Greek numeral ΚΒ´ Roman numeral XXII, xxii Binary 101102 Ternary...

distinct squares. However, it is divisible by the total number of its divisors, making it a refactorable number. The sum of Euler's totient function φ(x)...

Cardinal seventy-five Ordinal 75th (seventy-fifth) Factorization 3 × 52 Divisors 1, 3, 5, 15, 25, 75 Greek numeral ΟΕ´ Roman numeral LXXV, lxxv Binary 10010112...

sixty-six Ordinal 266th (two hundred sixty-sixth) Factorization 2 × 7 × 19 Divisors 1, 2, 7, 14, 19, 38, 133, 266 Greek numeral ΣΞϚ´ Roman numeral CCLXVI,...

number, and a lazy caterer number. There are 742 partitions of 30 into divisors of 30. the smallest number that is one more than triple its reverse. It...

many prime divisors will n have on average? What is the probability that it will have many more or many fewer divisors or prime divisors than the average...

Cardinal nine Ordinal 9th (ninth) Numeral system nonary Factorization 32 Divisors 1,3,9 Greek numeral Θ´ Roman numeral IX, ix Greek prefix ennea- Latin prefix...

constant function 1 ∗ 1 = σ0 = d = τ, where d = τ is the number of divisors of n, (see divisor function). Both of these lists of functions extend infinitely...

disproving) it. Some typical examples are as follows. (Others involve the divisor function σ(n).) The Riesz criterion was given by Riesz (1916), to the effect...

factorization ( 1 + i ) ( 1 − i ) {\displaystyle (1+i)(1-i)} Prime 1st Divisors 1, 2 Greek numeral Β´ Roman numeral II, ii Greek prefix di- Latin prefix...

Oman. 9999 is the largest 4-digit whole number. 9999 can be used as a divisor to generate 4-digit decimal recurrences. For example, 1234 / 9999 = 0.123412341234...

certain proportion of missed errors, due to the quotient ring having zero divisors. The advantage of choosing a primitive polynomial as the generator for...

Arakelov's original construction studies one such theory, where a definition of divisors is constructed for a scheme X {\displaystyle {\mathfrak {X}}} of relative...

second anti-perfect number, meaning that reversing the digits of the proper divisors of 244 and adding the results gives 244 back again. part of the sequence...

+ r D {\displaystyle K_{X}+rD} is in the closed real cone of effective divisors in the Néron–Severi group of X. If α is negative, then X is pseudo-canonical...

sixty-six Ordinal 666th (six hundred sixty-sixth) Factorization 2 × 32 × 37 Divisors 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666 Greek numeral ΧΞϚ´ Roman...

number if and only if n {\displaystyle n} is square-free, and for all prime divisors p {\displaystyle p} of ⁠ n {\displaystyle n} ⁠, it is true that ⁠ p − 1...

forty-three Ordinal 43rd (forty-third) Factorization prime Prime 14th Divisors 1, 43 Greek numeral ΜΓ´ Roman numeral XLIII, xliii Binary 1010112 Ternary...

→ Cardinal thirty-five Ordinal 35th (thirty-fifth) Factorization 5 × 7 Divisors 1, 5, 7, 35 Greek numeral ΛΕ´ Roman numeral XXXV, xxxv Binary 1000112 Ternary...

the ideal class group or divisor class group for Arakelov divisors. Arakelov divisor An Arakelov divisor (or replete divisor) on a global field is an...

a-b=1;\;} with a n − b n = 1 {\displaystyle a^{n}-b^{n}=1} having no prime divisors, n = 2 {\displaystyle n=2} , a + b {\displaystyle a+b\;} a power of two...

Ordinal 9801st (nine thousand eight hundred first) Factorization 34 × 112 Divisors 1, 3, 9, 11, 27, 33, 81, 99, 121, 297, 363, 891, 1089, 3267, 9801 Greek...

for a number c having many divisors, with ⁠b/2⁠ < c < b, replacing ⁠a/b⁠ by ⁠ac/bc⁠, and expanding ac as a sum of divisors of bc, similar to the method...

Ordinal 40th (fortieth) Numeral system quadragesimal Factorization 23 × 5 Divisors 1, 2, 4, 5, 8, 10, 20, 40 Greek numeral Μ´ Roman numeral XL, xl Latin prefix...

the operation that produces such a remainder when given a dividend and divisor. Alternatively, a remainder is also what is left after subtracting one...

458 = 2 × 229. It is a nontotient. There are 458partitions of 24 into divisors of 24. 459 = 33 × 17. It is a triangular matchstick number. 460 = 22 ×...

the natural number following 132 and preceding 134. 133 is an n whose divisors (excluding n itself) added up divide φ(n). It is an octagonal number and...

→ Cardinal sixty-two Ordinal 62nd (sixty-second) Factorization 2 × 31 Divisors 1, 2, 31, 62 Greek numeral ΞΒ´ Roman numeral LXII, lxii Binary 1111102...

coefficients of the Ramanujan modular form Divisor function, an arithmetic function giving the number of divisors of an integer This disambiguation page lists...

40 50 60 70 80 90 → Cardinal twenty-seven Ordinal 27th Factorization 33 Divisors 1, 3, 9, 27 Greek numeral ΚΖ´ Roman numeral XXVII, xxvii Binary 110112...

subset S of a ring R is called saturated if it is closed under taking divisors: i.e., whenever a product xy is in S, the elements x and y are in S too...

is worth noting that the traditional form of the divisor method, which involves using a fixed divisor and allowing the house size to vary, satisfies strong...

ALGOL 68, for example, give a positive remainder (or 0) even for negative divisors, and some programming languages, such as C90, leave it to the implementation...

Christianity and Hinduism. 12000 is an odd, composite number, which has 48 divisors. It is also a regular number, a 3 times decagonal number, a number in base...

Fig. 2: The lattice of divisors of 4, with the ordering "is divisor of", is atomic, with 2 being the only atom and coatom. It is not atomistic, since 4...

263. It has the prime factorization 2·131. There are four divisors of this number, the divisors being 1, 2, 131, and 262 itself, which makes it a semiprime...

An average order of d(n), the number of divisors of n, is log n; An average order of σ(n), the sum of divisors of n, is nπ2 / 6; An average order of φ(n)...

preceding 201. 200 is an abundant number, as 265, the sum of its proper divisors, is greater than itself. The number appears in the Padovan sequence, preceded...

In compiler theory, a greatest common divisor test (GCD test) is the test used in study of loop optimization and loop dependence analysis to test the...

thirty-one Ordinal 31st (thirty-first) Factorization prime Prime 11th Divisors 1, 31 Greek numeral ΛΑ´ Roman numeral XXXI, xxxi Binary 111112 Ternary...

two odd divisors, 3 and 9, and two polite representations 9 = 2 + 3 + 4 = 4 + 5; the politeness of 15 is 3 because it has three odd divisors, 3, 5, and...

ninety-seven Ordinal 297th (two hundred ninety-seventh) Factorization 33 × 11 Divisors 1, 3, 9, 11, 27, 33, 99, 297 Greek numeral ΣϞΖ´ Roman numeral CCXCVII,...

product of these integers, under the condition that the divisors are pairwise coprime (no two divisors share a common factor other than 1). The theorem is...

90 → Cardinal thirty Ordinal 30th (thirtieth) Factorization 2 × 3 × 5 Divisors 1, 2, 3, 5, 6, 10, 15, 30 Greek numeral Λ´ Roman numeral XXX, xxx Binary...

Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to n: ∑ k = 1 n d ( k ) n ≈ ln ⁡ n + 2 γ − 1...

Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia...

Ordinal 5th (fifth) Numeral system quinary Factorization prime Prime 3rd Divisors 1, 5 Greek numeral Ε´ Roman numeral V, v Greek prefix penta-/pent- Latin...

order dividing 2 to obtain a coprime factorization of the largest odd divisor of Δ in which Δ = −4ac or Δ = a(a − 4c) or Δ = (b − 2a)(b + 2a). If the...

1729th (one thousand seven hundred twenty-ninth) Factorization 7 × 13 × 19 Divisors 1, 7, 13, 19, 91, 133, 247, 1729 Greek numeral ,ΑΨΚΘ´ Roman numeral MDCCXXIX...

seventy-one Ordinal 71st (seventy-first) Factorization prime Prime 20th Divisors 1, 71 Greek numeral ΟΑ´ Roman numeral LXXI, lxxi Binary 10001112 Ternary...

power, then the ring of b {\displaystyle b} -adic numbers has no zero-divisors other than 0, so the only fixed points of f ( x ) = x 2 {\displaystyle...

isomorphism is part of the usual correspondence between Weil divisors and Cartier divisors.) Finally, the dual of the twisting sheaf corresponds to the...

Ordinal 18th (eighteenth) Numeral system octodecimal Factorization 2 × 32 Divisors 1, 2, 3, 6, 9, 18 Greek numeral ΙΗ´ Roman numeral XVIII, xviii Unicode...

Law, Annex II While D'Hondt uses 1,2,3,4,... as divisors, Macau instead uses 1,2,4,8,... as divisors, see article 17, 2) of the electoral law. Their method...

principal divisors, i.e., divisors of rational functions. This holds for fields that are not algebraically closed, provided one considers divisors and functions...

bad divisors the running time would double since each FDIV would take about 80 clock cycles instead of the usual 40 cycles. With more random divisors the...

one or more of its divisors. For instance, 30 has 13 multiplicative partitions, as a product of one divisor (30 itself), two divisors (for instance 6 ·...

ninety-nine Ordinal 299th (two hundred ninety-ninth) Factorization 13 × 23 Divisors 1, 13, 23, 299 Greek numeral ΣϞΘ´ Roman numeral CCXCIX, ccxcix Binary 1001010112...

→ Cardinal ninety-one Ordinal 91st (ninety-first) Factorization 7 × 13 Divisors 1, 7, 13, 91 Greek numeral ϞΑ´ Roman numeral XCI, xci Binary 10110112 Ternary...

fifty-three Ordinal 53rd (fifty-third) Factorization prime Prime 16th Divisors 1, 53 Greek numeral ΝΓ´ Roman numeral LIII, liii Binary 1101012 Ternary...

Sun, or year. Twelve is convenient because it has a maximal number of divisors among the numbers up to its double, a property only true of 1, 2, 6, 12...

normal variety X and a Q {\displaystyle \mathbb {Q} } -divisor D on X (e.g., canonical divisor), the discrepancy of the pair (X, D) measures the degree...

lattices. Consider the divisors of some composite number, such as (in the figure) 120, partially ordered by divisibility. Any two divisors of 120, such as 12...

(sixty-five thousand five hundred thirty-fifth) Factorization 3 × 5 × 17 × 257 Divisors 16 total Greek numeral M ϝ {\displaystyle {\stackrel {\digamma }{\mathrm...

{\displaystyle P(n)=\sum _{d\mid n}d\varphi (n/d)} where d {\displaystyle d} is a divisor of n {\displaystyle n} and φ {\displaystyle \varphi } is Euler's totient...

all odd prime divisors of Fn are congruent to 1 modulo 4, implying that all odd divisors of Fn (as the products of odd prime divisors) are congruent...

EXAMPLE a(3) = -8 because the divisors of 3 are {1, 3} and mu(1)*1^2 + mu(3)*3^2 = -8. a(4) = -3 because the divisors of 4 are {1, 2, 4} and mu(1)*1^2...

90 → Cardinal seventy Ordinal 70th (seventieth) Factorization 2 x 5 x 7 Divisors 1, 2, 5, 7, 10, 14, 35, 70 Greek numeral Ο´ Roman numeral LXX, lxx Binary...

Cardinal seventy-six Ordinal 76th (seventy-sixth) Factorization 22 × 19 Divisors 1, 2, 4, 19, 38, 76 Greek numeral ΟϚ´ Roman numeral LXXVI, lxxvi Binary...

2,\ldots ,n\}} , excluding the sets of integers divisible by the prime divisors. φ ( 20 ) = φ ( 2 2 5 ) = 20 ( 1 − 1 2 ) ( 1 − 1 5 ) = 20 ⋅ 1 2 ⋅ 4 5 =...

nonzero element has a multiplicative inverse, but which nonetheless has divisors of zero, that is, nonzero elements x, y such that xy = 0. A square matrix...

M p → ∞ {\displaystyle M_{p}\rightarrow \infty } , the number of prime divisors of M {\displaystyle M} in the interval [ A , B ] {\displaystyle [A,B]}...

formed by the Cayley-Dickson construction begin to have nontrivial zero divisors, in that this and every further algebra created by the construction will...

is a refactorable number since it is divisible by the total number of divisors it has, and in base 10 it is divisible by the sum of its digits, making...

In mathematics, division by zero, division where the divisor (denominator) is zero, is a problematic special case. Using fraction notation, the general...

thirty-seven Ordinal 37th (thirty-seventh) Factorization prime Prime 12th Divisors 1, 37 Greek numeral ΛΖ´ Roman numeral XXXVII, xxxvii Binary 1001012 Ternary...

Cardinal ninety-five Ordinal 95th (ninety-fifth) Factorization 5 × 19 Divisors 1, 5, 19, 95 Greek numeral ϞΕ´ Roman numeral XCV, xcv Binary 10111112 Ternary...

1. A001045 Sum of proper divisors s(n) 0, 1, 1, 3, 1, 6, 1, 7, 4, 8, ... s(n) = σ(n) − n is the sum of the proper divisors of the positive integer n...

Ordinal 50th (fiftieth) Numeral system quinquagesimal Factorization 2 × 52 Divisors 1, 2, 5, 10, 25, 50 Greek numeral Ν´ Roman numeral L, l Unicode symbol...

untouchable number because it is not equal to the sum of any number's proper divisors. 304 is a nontotient number because it is an even number and phi(x) = 304...

polygonal number. 273 is a deficient number, as the sum of its proper divisors (175) is less than itself. The number 273 has particular significance in...

n-queens problem for n = 11 is 671. 672 = 25 × 3 × 7. It is a harmonic divisor number, a Zuckerman number, an admirable number, a largely composite number...

seventy-nine Ordinal 79th (seventy-ninth) Factorization prime Prime 22nd Divisors 1, 79 Greek numeral ΟΘ´ Roman numeral LXXIX, lxxix Binary 10011112 Ternary...

irreducible divisors and a closed point on the special fiber of an arithmetic surface, we can define the local intersection index of the divisors at the point...

coefficients. It was discovered by Henry W. Gould in 1972. The greatest common divisors of the binomial coefficients forming each of the two triangles in the Star...

words a non-singular projective algebraic surface with ample anticanonical divisor class. They are in some sense the opposite of surfaces of general type...

σk(n) is the divisor function (i.e. the sum of the k-th powers of the divisors of n, including 1 and n). σ0(n), the number of divisors of n, is usually...

Unitary perfect Semiperfect Practical Descartes Erdős–Nicolas With many divisors Abundant Primitive abundant Highly abundant Superabundant Colossally abundant...

twenty-three Ordinal 1023rd (one thousand twenty-third) Factorization 3 × 11 × 31 Divisors 1, 3, 11, 31, 33, 93, 341, 1023 Greek numeral ,ΑΚΓ´ Roman numeral MXXIII...

both a and b, and such that every other common divisor of a and b divides d. All greatest common divisors of a and b are associated. Any UFD is integrally...

other integers cannot be roots of unity modulo n, because they are zero divisors modulo n. A primitive root modulo n, is a generator of the group of units...

nine hundred Ordinal 900th (nine hundredth) Factorization 22 × 32 × 52 Divisors 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90...

Rapoport, Michael; Yang, Tonghai (2020). "Modularity of generating series of divisors on unitary Shimura varieties". Astérisque. 421: 7–125. doi:10.24033/ast...

prime is a natural number that has exactly two distinct natural number divisors: 1 and itself. Prime or PRIME may also refer to: Prime (DC Comics), a...

ninety-seven Ordinal 97th (ninety-seventh) Factorization prime Prime 25th Divisors 1, 97 Greek numeral ϞΖ´ Roman numeral XCVII, xcvii Binary 11000012 Ternary...

seventy-three Ordinal 73rd (seventy-third) Factorization prime Prime 21st Divisors 1, 73 Greek numeral ΟΓ´ Roman numeral LXXIII, lxxiii Binary 10010012 Ternary...

field. In this case, the so-called divisor group is defined. It can be shown that the quotient of the set of all divisors of degree 0 {\displaystyle 0} by...

Cardinal thirty-nine Ordinal 39th (thirty-ninth) Factorization 3 × 13 Divisors 1, 3, 13, 39 Greek numeral ΛΘ´ Roman numeral XXXIX, xxxix Binary 1001112...

Cardinal sixty-six Ordinal 66th (sixty-sixth) Factorization 2 × 3 × 11 Divisors 1, 2, 3, 6, 11, 22, 33, 66 Greek numeral ΞϚ´ Roman numeral LXVI, lxvi Binary...

seventy-eight Ordinal 278th (two hundred seventy-eighth) Factorization 2 × 139 Divisors 1, 2, 139, 278 Greek numeral ΣΟΗ´ Roman numeral CCLXXVIII, cclxxviii Binary...

one Ordinal 1001st (one thousand [and] first) Factorization 7 × 11 × 13 Divisors 1, 7, 11, 13, 77, 91, 143, 1001 Greek numeral ,ΑΑ´ Roman numeral MI, mi...

f(x)} by x − r {\displaystyle x-r} , and x − r {\displaystyle x-r} is a divisor of f ( x ) {\displaystyle f(x)} if and only if f ( r ) = 0 {\displaystyle...

{\displaystyle \sigma _{3}} is the function that sums the cubes of the divisors of its argument: 1 3 + 2 3 + 3 3 + 6 3 = ( 1 3 + 2 3 ) ( 1 3 + 3 3 ) =...

specify that V is a non-singular projective surface, and let H be the divisor class on V of a hyperplane section of V in a given projective embedding...

of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám's problem...

common divisors Extended Euclidean algorithm, a method for solving the Diophantine equation ax + by = d where d is the greatest common divisor of a and...

bundles are in bijection with linear equivalences class of divisors, and given a divisor D on X with associated line bundle O(D), the class c1(O(D))...

zero divisors is isomorphic to the real or complex numbers. Every commutative real unital Noetherian Banach algebra (possibly having zero divisors) is...

f\colon Y\to X} be a resolution of singularities of X. Using that Cartier divisors can be pulled back, one can write K Y = f ∗ ( K X ) + ∑ i a i E i {\displaystyle...

Algorithm Generates Traditional Musical Rhythms". The greatest common divisor of two numbers is used rhythmically giving the number of beats and silences...

Positive integers that have a property about their divisors...

nine Ordinal 109th (one hundred ninth) Factorization prime Prime 29th Divisors 1, 109 Greek numeral ΡΘ´ Roman numeral CIX, cix Binary 11011012 Ternary...

Cardinal forty-eight Ordinal 48th (forty-eighth) Factorization 24 × 3 Divisors 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Greek numeral ΜΗ´ Roman numeral XLVIII...

price, not market capitalisation. Therefore, a fudge factor called the "Divisor" is used to ensure that the index value only changes when stock prices...

Sierra del Divisor National Park (Spanish: Parque Nacional Sierra del Divisor) is a national park in the Amazon rainforest of Peru, established in 2015...

(1 2 4), (1 4 2), (1 3 4), (1 4 3), (2 3 4), (2 4 3)}. |A4| = 12 so the divisors are 1, 2, 3, 4, 6, 12. Assume to the contrary that there exists a subgroup...

di are the sizes of the non-trivial conjugacy classes; these are proper divisors of |G| bigger than one, and they are also equal to the indices of the centralizers...

formula shows that the canonical class of C is the intersection product of divisors of bidegrees (d1,d2) and (d1−2,d2−2). The intersection form on P1×P1 is...

union of coordinate hyperplanes. There are two variants of the concept, a divisor with normal crossings or with simple normal crossings. These can be considered...

2023-07-24. Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS...

Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia...

{\displaystyle \sigma ^{2}(n)=\sigma (\sigma (n))=2n\,,} where σ is the sum-of-divisors function. Superperfect numbers are not a generalization of perfect numbers...

90 → Cardinal sixty-four Ordinal 64th (sixty-fourth) Factorization 26 Divisors 1, 2, 4, 8, 16, 32, 64 Greek numeral ΞΔ´ Roman numeral LXIV, lxiv Binary...

Cardinal seventy-four Ordinal 74th (seventy-fourth) Factorization 2 × 37 Divisors 1, 2, 37, 74 Greek numeral ΟΔ´ Roman numeral LXXIV, lxxiv Binary 10010102...

(forty-seventh) Numeral system heptaquadragesimal Factorization prime Prime 15th Divisors 1, 47 Greek numeral ΜΖ´ Roman numeral XLVII, xlvii Binary 1011112 Ternary...

pair of amicable numbers with 220. That means that the sum of the proper divisors are the same between the two numbers. 284 can be written as a sum of exactly...

The Sierra del Divisor Reserved Zone (Spanish: Zona Reservada Sierra del Divisor) is a protected area located in the Loreto Region of Peru, covering territories...

Cardinal ninety-eight Ordinal 98th (ninety-eighth) Factorization 2 × 72 Divisors 1, 2, 7, 14, 49, 98 Greek numeral ϞΗ´ Roman numeral XCVIII, xcviii Binary...

(seventeenth) Numeral system septendecimal Factorization prime Prime 7th Divisors 1, 17 Greek numeral ΙΖ´ Roman numeral XVII, xvii Binary 100012 Ternary...

the number of factors (divisors) of b n {\displaystyle b^{n}} , the nth power of the base b (although this includes the divisor 1, which does not produce...

number that is not the sum of some of its proper, nontrivial (i.e. >1) divisors (sequence A122036 in the OEIS). 351,352 = Kaprekar number 355,419 = Keith...

symbol is ‰, similar to a per cent sign % but with an extra zero in the divisor. Major dictionaries do not agree on the spelling, giving other options...

composite numbers, definition (1): numbers n where d(n), the number of divisors of n (A000005), increases to a record.)". The On-Line Encyclopedia of Integer...

ninety-five Ordinal 295th (two hundred ninety-fifth) Factorization 5 × 59 Divisors 1, 5, 59, 295 Greek numeral ΣϞΕ´ Roman numeral CCXCV, ccxcv Binary 1001001112...

element Δ of M is said to be a Garside element if the set of all right divisors of Δ, { r ∈ M ∣ for some  x ∈ M , Δ = x r } , {\displaystyle \{r\in M\mid...

90 → Cardinal −1, minus one, negative one Ordinal −1st (negative first) Divisors 1 Arabic −١ Chinese numeral 负一，负弌，负壹 Bengali −১ Binary (byte) S&M: 1000000012...

90 → Cardinal eighty-one Ordinal 81st (eighty-first) Factorization 34 Divisors 1, 3, 9, 27, 81 Greek numeral ΠΑ´ Roman numeral LXXXI, lxxxi Binary 10100012...

number that is not perfect, but that equals one of the partial sums of its divisors. That is, a number n is an Erdős–Nicolas number when there exists another...

{\sigma (n)}{n}}} where σ denotes the sum-of-divisors function (i.e., the sum of all positive divisors of n, including n itself). The first few superabundant...

Ordinal 101st (one hundred [and] first) Factorization prime Prime 26th Divisors 1, 101 Greek numeral ΡΑ´ Roman numeral CI Binary 11001012 Ternary 102023...

eighty-seven Ordinal 287th (two hundred eighty-seventh) Factorization 7 × 41 Divisors 1, 7, 41, 287 Greek numeral ΣΠΖ´ Roman numeral CCLXXXVII, cclxxxvii Binary...

four basic arithmetical operations, working with fractions, and finding divisors. In the early 1950s, Caleb Gattegno popularised this set of coloured number...

hundred five Ordinal 105th (one hundred fifth) Factorization 3 × 5 × 7 Divisors 1, 3, 5, 7, 15, 21, 35, 105 Greek numeral ΡΕ´ Roman numeral CV, cv Binary...

Ordinal 151st (one hundred fifty-first) Factorization prime Prime 36th Divisors 1, 151 Greek numeral ΡΝΑ´ Roman numeral CLI, cli Binary 100101112 Ternary...

indices that have no common divisors (i.e. are relative prime). Conversely, every set of Miller indices without common divisors defines a family of lattice...

super-Poulet number 4688 – 2-automorphic number 4689 – sum of divisors and number of divisors are both triangular numbers 4691 – balanced prime 4692 – pronic...

because the restriction of the divisors sum to members of S {\displaystyle {\mathcal {S}}} either decreases the divisors sum or leaves it unchanged. The...

(xy) as zero-divisors, but no non-zero nilpotent elements. As another example, the ring Z × Z contains (1, 0) and (0, 1) as zero-divisors, but contains...

quasi-amicable numbers are two positive integers such that the sum of the proper divisors of either number is one more than the value of the other number. In other...

municipality contains 5% of the 846,633-hectare (2,092,080-acre) Serra do Divisor National Park, created in 1989. It contains most of the Alto Juruá Extractive...

curves but on divisors and the Jacobian. Let C {\displaystyle C} be a hyperelliptic curve of genus g over a finite field K. A divisor D {\displaystyle...

Jacobian is a commutative algebraic group associated to a curve with a divisor, generalizing the Jacobian variety of a complete curve. They were introduced...

Cardinal sixty-eight Ordinal 68th (sixty-eighth) Factorization 22 × 17 Divisors 1, 2, 4, 17, 34, 68 Greek numeral ΞΗ´ Roman numeral LXVIII, lxviii Binary...

Cardinal fifty-nine Ordinal 59th (fifty-ninth) Factorization prime Prime 17th Divisors 1, 59 Greek numeral ΝΘ´ Roman numeral LIX, lix Binary 1110112 Ternary 20123...

were proved by Lee, Li, Rabideau and Schiffler in 2023. None of the prime divisors of a Markov number is congruent to 3 modulo 4, which implies that an odd...

division is an abbreviated form of long division suitable for one-digit divisors. Chunking – also known as the partial quotients method or the hangman method –...

an odd composite number with two prime factors. 265's sum of its proper divisors is 59. 265 is the number of derangements possible with 6 digits. That means...

using the divisor method from women-only lists at the national level. 47 elected via closed-list proportional representation using the divisor method at...

numbers to get a 16-digit result divide a 16-digit number by an 8-digit divisor Addition or subtraction is performed in a single step, with a turn of the...

fifty-three Ordinal 153rd (one hundred fifty-third) Factorization 32 × 17 Divisors 1, 3, 9, 17, 51, 153 Greek numeral ΡΝΓ´ Roman numeral CLIII, cliii Binary...

Cardinal forty-four Ordinal 44th (forty-fourth) Factorization 22 × 11 Divisors 1, 2, 4, 11, 22, 44 Greek numeral ΜΔ´ Roman numeral XLIV, xliv Binary 1011002...

90 → Cardinal forty-six Ordinal 46th (forty-sixth) Factorization 2 × 23 Divisors 1, 2, 23, 46 Greek numeral ΜϚ´ Roman numeral XLVI, xlvi Binary 1011102...

does not work well over more general rings, for if the ring contains zero-divisors then the only module satisfying this condition is the zero module. Over...

graphs with eight edges. 207 is a deficient number, as 207's proper divisors (divisors not including the number itself) only add up to 105: 1 + 3 + 9 + 23...

forty-three Ordinal 143rd (one hundred forty-third) Factorization 11 × 13 Divisors 1, 11, 13, 143 Greek numeral ΡΜΓ´ Roman numeral CXLIII, cxliii Binary 100011112...

LADSPA is unusual in that it attempts to provide only the "Greatest Common Divisor" of other standards. This means that its scope is limited, but it is simple...

divisors modulo principal divisors to the group of isomorphism classes of line bundles. A divisor corresponding to ωX is called the canonical divisor...

Cardinal thirty-eight Ordinal 38th (thirty-eighth) Factorization 2 × 19 Divisors 1, 2, 19, 38 Greek numeral ΛΗ´ Roman numeral XXXVIII, xxxviii Binary 1001102...

Ordinal 3rd (third) Numeral system ternary Factorization prime Prime 2nd Divisors 1, 3 Greek numeral Γ´ Roman numeral III or iii Latin prefix tre-/ter- Binary...

830,773,351,885,970,528,324,860,512,791,691,264. It has 8128 positive divisors, which all add up to 2126(2127-1), the 12th even perfect number (by the...

124 is an untouchable number, meaning that it is not the sum of proper divisors of any positive number. It is a stella octangula number, the number of...

every divisor of | G | {\displaystyle |G|} arises as the order of a subgroup of G {\displaystyle G} . Cauchy's theorem states that for any prime divisor p...

{\displaystyle \sigma _{p}(n)} is the divisor sum function, i.e. the sum of the p {\displaystyle p} -th powers of the divisors of n {\displaystyle n} . In particular...

in 1809. The rule is a special case of synthetic division in which the divisor is a linear monic factor. The rule establishes a method for dividing the...

mathematics, by sigma function one can mean one of the following: The sum-of-divisors function σa(n), an arithmetic function Weierstrass sigma function, related...

16560, 41472, 82311, 27441, 12209, 451, 53, 1, 0. The factors, also called divisors, of 2520 are: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24...

geometry, a Mori dream space is a projective variety whose cone of effective divisors has a well-behaved decomposition into certain convex sets called "Mori...

n-powersmooth numbers. In fact, the n-powersmooth numbers are exactly the positive divisors of “the least common multiple of 1, 2, 3, …, n” (sequence A003418 in the...

hundred fifty Ordinal 150th (one hundred fiftieth) Factorization 2 × 3 × 52 Divisors 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150 Greek numeral ΡΝ´ Roman numeral...

in three variables) that corresponds to a cubic divisor in the projective space P2. If the cubic divisor happens to be an elliptic curve, then the algebra...

and since 125 + 1 is σ3(5), 126 is the fifth value of the sum of cubed divisors function. 126 is the fifth S {\displaystyle {\mathcal {S}}} -perfect Granville...

some real number }}H\}.} Divisor methods differ by the method they use for rounding. A divisor method is parametrized by a divisor function d ( k ) {\displaystyle...

divisible only by themselves and 1. For any square-free number n, its divisors form a Boolean algebra that is a sublattice of the division lattice. The...

topological notion of a line bundle. Due to their interactions with Cartier divisors, they play a central role in the study of algebraic varieties. Let (X,...

set of three different numbers so related that the restricted sum of the divisors of each is equal to the sum of the other two numbers. In another equivalent...

hundred four Ordinal 204th (two hundred fourth) Factorization 22 × 3 × 17 Divisors 1, 2, 3, 4, 6, 12, 17, 34, 51, 68, 102, 204 Greek numeral ΣΔ´ Roman numeral...

exactly two divisors: 1 and itself. The first 100 prime numbers are: A highly composite number (HCN) is a positive integer with more divisors than any smaller...

the process of breaking down a composite number into smaller non-trivial divisors A coefficient, a multiplicative factor in an expression, usually a number...

seventy-one Ordinal 171st (one hundred seventy-first) Factorization 32 × 19 Divisors 1, 3, 9, 19, 57, 171 Greek numeral ΡΟΑ´ Roman numeral CLXXI, clxxi Binary...

= 2, B = 2, C = 1 Same as Sainte-Laguë but first divisor is 1.4 to favour larger parties. Divisors: 1.4, 3, 5, ... Result: A = 2, B = 2, C = 1 The Hare...

eighty-nine Ordinal 89th (eighty-ninth) Factorization prime Prime 24th Divisors 1, 89 Greek numeral ΠΘ´ Roman numeral LXXXIX, lxxxix Binary 10110012 Ternary...

Fortunate Other prime factor or divisor related numbers Blum Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael...

such that the sum of all divisors of n (the sum-of-divisors function σ(n)) is equal to 2n − 1, the sum of all proper divisors of n, s(n) = σ(n) − n, then...

"rolling" two-year period with a maximum of 52 tournaments and a minimum divisor of 40 events. During 2018, nearly 400 tournaments on 20 tours were covered...

coprimes below it, so it is a noncototient. And it is not the sum of proper divisors of any number, making it an untouchable number. There are 146 connected...

numbers as the field of fractions of the integers. For rings that have zero divisors, the construction is similar but requires more care. Localization is commonly...

Cardinal eighty-two Ordinal 82nd (eighty-second) Factorization 2 × 41 Divisors 1, 2, 41, 82 Greek numeral ΠΒ´ Roman numeral LXXXII, lxxxii Binary 10100102...

twenty-two Ordinal 222nd (two hundred twenty-second) Factorization 2 × 3 × 37 Divisors 1, 2, 3, 6, 37, 74, 111, 222 Greek numeral ΣΚΒ´ Roman numeral CCXXII, ccxxii...

forty-four Ordinal 144th (one hundred forty-fourth) Factorization 24 × 32 Divisors 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Greek numeral ΡΜΔ´...

eighty-nine Ordinal 289th (two hundred eighty-ninth) Factorization 172 Divisors 1, 17, 289 Greek numeral ΣΠΘ´ Roman numeral CCLXXXIX, cclxxxix Binary 1001000012...

positive divisors of n {\displaystyle n} , σ 1 ( n ) = σ ( n ) {\displaystyle \sigma _{1}(n)=\sigma (n)} , the sum of all the positive divisors of n {\displaystyle...

zero divisors. A finite-dimensional unital associative algebra (over any field) is a division algebra if and only if it has no nonzero zero divisors. Indeed...

multiples. The least common multiple can be computed from the greatest common divisor (gcd) with the formula lcm ⁡ ( a , b ) = | a b | gcd ( a , b ) . {\displaystyle...

→ Cardinal forty-five Ordinal 45th (forty-fifth) Factorization 32 × 5 Divisors 1, 3, 5, 9, 15, 45 Greek numeral ΜΕ´ Roman numeral XLV, xlv Binary 1011012...

significance in Judaism and Christianity. The number 318 has the proper divisors 1, 2, 3, 6, 53, 106, and 159. It is an abundant number, a sphenic number...

constant, the constant d is a common divisor in S of a and b; we shall show it is in fact a greatest common divisor by showing that it lies in aS + bS....

2]. Sloane, N. J. A. (ed.). "Sequence A005101 (Abundant numbers (sum of divisors of m exceeds 2m).)". The On-Line Encyclopedia of Integer Sequences. OEIS...

surface to be very ample. Let D be a nef divisor on a smooth projective surface X. Denote by KX the canonical divisor of X. If D2 > 4, then the linear system...

9855th (nine thousand eight hundred fifty-fifth) Factorization 33 × 5 × 73 Divisors 1, 3, 5, 9, 15, 27, 45, 73, 135, 219, 365, 657, 1095, 1971, 3285, 9855...

{\displaystyle \sum _{d\mid n}|\mu (d)|=2^{\omega (n)}} is the number of unitary divisors. (sequence A034444 in the OEIS) ∑ d ∣ n | μ ( d ) | k ω ( d ) = ( k + 1...

algebraic geometry, the Ramanujam–Samuel theorem gives conditions for a divisor of a local ring to be principal. It was introduced independently by Samuel (1962)...

Carl Friedrich Gauss: Gauss's lemma (polynomials), the greatest common divisor of the coefficients is a multiplicative function Gauss's lemma (number...

No element can have a prime divisor p {\displaystyle p} of the form p = 8 k + 3 {\displaystyle p=8k+3} . All prime divisors p {\displaystyle p} of the...

preceding 231. Additionally, 230 is: a composite number, with its proper divisors being 1, 2, 5, 10, 23, 46, and 115. a sphenic number because it is the...

Gauss's lemma underlies all the theory of factorization and greatest common divisors of such polynomials. Gauss's lemma first appeared as Article 42 in his...

forty-seven Ordinal 147th (one hundred forty-seventh) Factorization 3 × 72 Divisors 1, 3, 7, 21, 49, 147 Greek numeral ΡΜΖ´ Roman numeral CXLVII, cxlvii Binary...

idempotents 1 2 ( 1 ± j ) {\textstyle {\frac {1}{2}}(1\pm j)} and zero divisors ⁠ ( 1 + j ) ( 1 − j ) = 0 {\displaystyle (1+j)(1-j)=0} ⁠, so such algebras...

elementary divisors of M, and the Jordan normal form is concerned with representing M in terms of blocks associated to the elementary divisors. The proof...

633-hectare (2,092,080-acre) Serra do Divisor National Park, created in 1989. IBGE 2020 PARNA da Serra do Divisor (in Portuguese), ISA: Instituto Socioambiental...

number theory that deals with prime numbers and with factorization and divisors. The focus is usually on developing approximate formulas for counting these...

Hurwitz quaternions of given positive norm n is 24 times the sum of the odd divisors of n. The generating function of the numbers c(n) is given by the level...

divisors may be used to find a generator of any ideal. More generally, any two principal ideals in a commutative ring have a greatest common divisor in...

eighty-nine Ordinal 1089th (one thousand eighty-ninth) Factorization 32 × 112 Divisors 1, 3, 9, 11, 33, 99, 121, 363, 1089 Greek numeral ,ΑΠΘ´ Roman numeral MLXXXIX...

twenty-three Ordinal 123rd (one hundred twenty-third) Factorization 3 × 41 Divisors 1, 3, 41, 123 Greek numeral ΡΚΓ´ Roman numeral CXXIII, cxxiii Binary 11110112...

the set of effective Weil divisors on X that are linearly equivalent to D. The same definition is used if D is a Cartier divisor on a complete variety over...

modulus of a prescaler is its frequency divisor. A dual-modulus prescaler has two separate frequency divisors, usually M and M+1. A frequency synthesizer...

related to a product of two curves and are not a complete intersection of divisors in an Abelian variety. The Fano surface S of a smooth cubic threefold F...

Search (GIMPS). A prime number is a natural number greater than 1 with no divisors other than 1 and itself. Euclid's theorem proves that for any given prime...

v_dividend; ;divisor = 2 mvi a,02h; sta v_divisor; ;zera result mvi a,00h; sta v_result; ;load the values to BC lda v_dividend; mov b,a; lda v_divisor; mov c...

3511th (three thousand five hundred eleventh) Factorization prime Prime Yes Divisors 1, 3511 Greek numeral ,ΓΦΙΑ´ Roman numeral MMMDXI, mmmdxi Binary 1101101101112...

{\sigma (m)}{m}}>5} , where σ ( m ) {\displaystyle \sigma (m)} = sum of divisors of m 123,456,789 = smallest zeroless base-10 pandigital number 126,390...

surveying ship "Cartier", a song by Bazzi from the album Cosmic Cartier divisor in algebraic geometry Port-Cartier, Quebec Cartier Racing Award, for horseracing...

Cardinal fifty-eight Ordinal 58th (fifty-eighth) Factorization 2 × 29 Divisors 1, 2, 29, 58 Greek numeral ΝΗ´ Roman numeral LVIII, lviii Binary 1110102...

over the positive divisors of n. Hence those divisors form a Boolean algebra. These divisors are not subsets of a set, making the divisors of n a Boolean...

{\displaystyle p} at once (see below), and happen to coincide with the prime divisors of the order of the Monster group. Andrew Ogg (1975) proved that a prime...

equivalence class of Weil divisors on X. Any such divisor is called the canonical divisor KX. For a normal scheme X, the canonical divisor KX is said to be Q-Cartier...

been using V/1.2. That is, the modified method changes the sequence of divisors used in this method from (1, 3, 5, 7, ...) to (1.4, 3, 5, 7, ...). This...

theorem). In algebraic number theory Kronecker introduced the theory of divisors as an alternative to Dedekind's theory of ideals, which he did not find...

Certain non-zero integers map to zero in certain rings. The lack of zero divisors in the integers (last property in the table) means that the commutative...

hundred fifteen Ordinal 215th (two hundred fifteenth) Factorization 5 × 43 Divisors 1, 5, 43, 215 Greek numeral ΣΙΕ´ Roman numeral CCXV, ccxv Binary 110101112...

90 → Cardinal fifty-one Ordinal 51st (fifty-first) Factorization 3 × 17 Divisors 1, 3, 17, 51 Greek numeral ΝΑ´ Roman numeral LI, li Binary 1100112 Ternary...

{\displaystyle 3^{3}\cdot 5^{5}\cdot 7^{7}} . Find the number of positive integer divisors of n {\displaystyle n} . Note that 149 − 2 = 147 = 3 ⋅ 7 2 {\displaystyle...

that state, also using the Sainte-Laguë method. For each calculation, a divisor is chosen by the Federal Returning Officer so that the total number of...

triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple...

which is one more than a primorial 30203 = safe prime 30240 = harmonic divisor number, smallest 4-perfect number 30323 = Sophie Germain prime and safe...

zero of Mertens function and a nontotient. The sum of the squares of the divisors of 26 is 850 (sequence A001157 in the OEIS). The maximum possible Fair...

forty thousand Ordinal 40000th (forty thousandth) Factorization 26 × 54 Divisors 35 total Greek numeral M δ {\displaystyle {\stackrel {\delta }{\mathrm...

algorithm for the greatest common divisor of two integers x and y is certifying: it outputs three integers g (the divisor), a, and b, such that ax + by =...

filter-like topological generalization of a sequence Net, a linear system of divisors of dimension 2 Net (polyhedron), an arrangement of polygons that can be...

states that this is equivalent to a divisor in the class being the sum of an ample divisor and an effective divisor. Bombieri–Lang conjecture Lang, Serge...

so many small prime factors, it is the smallest number with exactly 14 divisors, namely 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96 and 192. Because its...

of theta divisors and translates of the curve C {\displaystyle C} . There is a 1-1 correspondence between pairs of odd symmetric theta divisors and 2-torsion...

states that if x and y are coprime integers (i.e. they share no common divisors other than 1 and −1) there exist integers r and s such that r x + s y =...

it is a non-repetitive Kaprekar number. It is also the sum of all the divisors of 100 and the number of week-month combinations in the Gregorian calendar...

to any nonzero commutative rng R {\displaystyle R} with no nonzero zero divisors. The embedding is given by r ↦ r s s {\displaystyle r\mapsto {\frac {rs}{s}}}...

number of divisors of n {\displaystyle n} which are congruent to 1 modulo 4 and d 3 ( n ) {\displaystyle d_{3}(n)} is the number of divisors of n {\displaystyle...