Definition:Divisor Function

Definition
The divisor function:


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

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

Also see

 * Definition:Divisor Counting Function: $\map {\sigma_0} n$ is the number of divisors of $n$ and is frequently written $\map d n$, or $\map \tau n$


 * Definition:Sigma Function: $\map {\sigma_1} n$ is the sum of the divisors of $n$ and is frequently written $\map \sigma n$