Definition:Divisor Function

Definition
The divisor function:


 * $\displaystyle \sigma_\alpha \left({n}\right) = \sum_{m \mathop \backslash n} m^\alpha$

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

Also see

 * Definition:Tau Function: $\sigma_0 \left({n}\right)$ is the number of divisors of $n$ and is frequently written $d \left({n}\right)$, or $\tau \left({n}\right)$


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