DivisorSum(f(k), For(k, n)), rendered as ∑k∣nf(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 ∑k∣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 | ∑k∣nf(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."))