Definition:Sum Over Divisors

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Definition

Let $n$ be a positive integer.

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


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

Then the sum of $\map f d$ over all the divisors of $n$ is denoted:

$\displaystyle \sum_{d \mathop \divides n} \map f d$


Thus, for example:

$\displaystyle \sum_{d \mathop \divides 10} \map f d = \map f 1 + \map f 2 + \map f 5 + \map f {10}$