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

Operators