# Definition:Divisor Function

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## Definition

The **divisor function**:

- $\displaystyle \map {\sigma_\alpha} n = \sum_{m \mathop \divides n} m^\alpha$

(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 $\map \sigma n$