Definition:Divisor Function

Definition
Let $\alpha \in \Z_{\ge 0}$ be a non-negative integer.

A divisor function is an arithmetic function of the form:


 * $\ds \map {\sigma_\alpha} n = \sum_{m \mathop \divides n} m^\alpha$

where the summation is taken over all $m \le n$ such that $m$ divides $n$).

There exist the following special cases: