SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

DivisorSum

DivisorSum[n, form]
represents the sum of form[i] for all i that divide n.

DivisorSum[n, form, cond]
includes only those divisors for which cond[i] gives True.

DivisorSum[n, form] is equivalent to Sum[form[d], {d, Divisors[n]}] for positive n.

DivisorSum[n, form, cond] is automatically simplified when n is a positive integer.

DivisorSum[n, form] is automatically simplified when form is a polynomial function.

Evaluate at positive integers:

Exact values are generated at positive integers:

Conditions on divisors can be specified:

DivisorSum works on formal expressions:

DivisorSum works for symbolic argument:

DivisorSum automatically simplifies for polynomial functions:

Closed forms:

Compute the Lambert series for Euler totient function:

Number of polynomials over

that are irreducible of degree n:

Distribution of irreducible polynomials modulo 5:

Logarithmic plot of the count for p=2, 3, 5:

Twisted divisor sum:

Define the unitary convolution:

Sum of squares:

The arguments to DivisorSum are not affected by N:

After evaluation, results may be affected by N:

The function f is applied to the divisors:

Only divisors that explicitly yield True on the conditions are used: