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:
- $\ds \sum_{d \mathop \divides n} \map f d$
Thus, for example:
- $\ds \sum_{d \mathop \divides 10} \map f d = \map f 1 + \map f 2 + \map f 5 + \map f {10}$