$\sigma$ function

Given a positive integer $n$, the sum of the integers 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
Canonical name	sigmaFunction
Date of creation	2013-03-22 16:07:12
Last modified on	2013-03-22 16:07:12
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	8
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A25
Synonym	divisor sigma
Synonym	sum of divisors function
Synonym	${\sigma }_1$ function