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The odd divisor function sigma_k^((o))(n)=sum_(d|n; d odd)d^k (1) is the sum of kth powers of the odd divisors of a number n. It is the analog of the divisor function for odd ...

There are two different statements, each separately known as the greatest common divisor theorem. 1. Given positive integers m and n, it is possible to choose integers x and ...

In 1657, Fermat posed the problem of finding solutions to sigma(x^3)=y^2, and solutions to sigma(x^2)=y^3, where sigma(n) is the divisor function (Dickson 2005). The first ...

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

An integer n which is tested to see if it divides a given number.

A nonzero element x of a ring for which x·y=0, where y is some other nonzero element and the multiplication x·y is the multiplication of the ring. A ring with no zero ...

Given an amicable pair (m,n), the quantity sigma(m) = sigma(n) (1) = =s(m)+s(n) (2) = m+n (3) is called the pair sum, where sigma(n) is the divisor function and s(n) is the ...

If a and b are integers not both equal to 0, then there exist integers u and v such that GCD(a,b)=au+bv, where GCD(a,b) is the greatest common divisor of a and b.

Any finite semigroup is a divisor for an alternating wreath product of finite groups and semigroups.

An aliquot sequence computed using the analog of the restricted divisor function s^*(n) in which only unitary divisors are included.