# Definition:Sum Over Divisors

## Definition

Let $n$ be a positive integer.

Let $f: \Z_{>0} \to \Z_{>0}$ be a function on the positive integers.

Let $d \mathrel \backslash n$ denote that $d$ is a divisor of $n$.

Then the sum of $f \left({d}\right)$ over all the divisors of $n$ is denoted:

$\displaystyle \sum_{d \mathop \backslash n} f \left({d}\right)$

Thus, for example:

$\displaystyle \sum_{d \mathop \backslash 10} f \left({d}\right) = f \left({1}\right) + f \left({2}\right) + f \left({5}\right) + f \left({10}\right)$