Definition:Divisor Function

Definition

The divisor function:

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

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

• $\sigma_0 \left({n}\right)$ is the number of divisors of $n$ and is frequently written $d \left({n}\right)$, or $\tau \left({n}\right)$ as specified in the definition of the tau function.

• $\sigma_1 \left({n}\right)$ is the sum of the divisors of $n$ and is frequently written $\sigma \left({n}\right)$ as specified in the definition of the sigma function.