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