# Fungrim entry: 8baf79

Symbol: DivisorSum $\sum_{k \mid n} f(k)$ Sum over divisors
DivisorSum(f(k), For(k, n)), rendered as $\sum_{k \mid n} f(k)$, represents the sum of $f(k)$ taken over all positive integers $k$ dividing the integer $n$.
DivisorSum(f(k), For(k, n), P(k)), rendered as $\sum_{k \mid n,\, P(k)} f(k)$, represents the sum of $f(k)$ taken over all positive integers $k$ dividing the integer $n$ and satisfying the predicate $P(k)$.
The special expression For(k, n) defines k as a locally bound variable.
The empty sum is equal to zero.
Definitions:
Fungrim symbol Notation Short description
DivisorSum$\sum_{k \mid n} f(k)$ Sum over divisors
Source code for this entry:
Entry(ID("8baf79"),
SymbolDefinition(DivisorSum, DivisorSum(f(k), For(k, n)), "Sum over divisors"),
Description(SourceForm(DivisorSum(f(k), For(k, n))), ", rendered as ", DivisorSum(f(k), For(k, n)), ", represents the sum of", f(k), "taken over all positive integers", k, "dividing the integer", n, "."),
Description(SourceForm(DivisorSum(f(k), For(k, n), P(k))), ", rendered as ", DivisorSum(f(k), For(k, n), P(k)), ", represents the sum of", f(k), "taken over all positive integers", k, "dividing the integer", n, "and satisfying the predicate", P(k), "."),
Description("The special expression", SourceForm(For(k, n)), "defines", SourceForm(k), "as a locally bound variable."),
Description("The empty sum is equal to zero."))

## Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC