# $\sigma$ function

Given a positive integer $n$, the sum of the integers $0 such that $d|n$ is the value of the sum of divisors function for $n$, often symbolized by a Greek lowercase $\sigma$. Thus,

 $\sigma(n)=\sum_{d|n}d.$

Sometimes this function is referred to as $\sigma_{1}(n)$, highlighting its relation to the divisor function.

Given coprime integers $m$ and $n$ (that is, $\gcd(m,n)=1$) then $\sigma(mn)=\sigma(m)\sigma(n)$, meaning that the sum of divisors function is a multiplicative function.

Title $\sigma$ function sigmaFunction 2013-03-22 16:07:12 2013-03-22 16:07:12 CompositeFan (12809) CompositeFan (12809) 8 CompositeFan (12809) Definition msc 11A25 divisor sigma sum of divisors function $\sigma_{1}$ function