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 the...

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...

In mathematics, a divisor of an integer n , {\displaystyle n,} also called a factor of n , {\displaystyle n,} is an integer m {\displaystyle m} that may...

In mathematics, the greatest common divisor (GCD) of two or more integers, which are not all zero, is the largest positive integer that divides each of...

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

has two distinct factors (itself and 1). Therefore, the number-of-divisors function d ( n ) {\displaystyle d(n)} of positive integers n {\displaystyle...

prime-counting functions. This article provides links to functions of both classes. An example of an arithmetic function is the divisor function whose value...

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...

called Euler's phi function. In other words, it is the number of integers k in the range 1 ≤ k ≤ n for which the greatest common divisor gcd(n, k) is equal...

integers. Equivalently, it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime, or...

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

mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b a {\displaystyle {\frac {b}{a}}}...

divisors of the numbers 1 to 1000. A divisor of an integer n is an integer m, for which n/m is again an integer (which is necessarily also a divisor of...

number 1: for instance, the formulas for Euler's totient function or for the sum of divisors function are different for prime numbers than they are for 1....

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

exactly eight divisors. All sphenic numbers are by definition squarefree, because the prime factors must be distinct. The Möbius function of any sphenic...

positive divisors; in symbols, σ 1 ( n ) = 2 n {\displaystyle \sigma _{1}(n)=2n} where σ 1 {\displaystyle \sigma _{1}} is the sum-of-divisors function. This...

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 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...

functions with a specified divisor. The functions half and third curry the divide function with a fixed divisor. The divisor function also forms a closure by...

if n is not square-free σk(n): the divisor function, which is the sum of the k-th powers of all the positive divisors of n (where k may be any complex number)...

\ldots )=F_{\gcd(a,b,c,\ldots )}\,} where gcd is the greatest common divisor function. In particular, any three consecutive Fibonacci numbers are pairwise...

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...

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

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 of all the proper divisors of any positive integer. That is, these numbers are not in the image of the aliquot sum function. Their study goes back...

frontotemporal lobar degeneration, and chronic traumatic encephalopathy Divisor function in number theory, also denoted d or σ0 Golden ratio (1.618...), although...

where we have the special case identity for the generating function of the divisor function, d(n) ≡ σ0(n), given by ∑ n = 1 ∞ x n 1 − x n = ∑ n = 1 ∞ x...

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 for...

the Mertens function suggests asymptotic bounds obtained by considering the Piltz divisor problem, which generalizes the Dirichlet divisor problem of computing...