This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# DivisorSum

 DivisorSum represents the sum of for all i that divide n. DivisorSumincludes only those divisors for which gives True.
• n can be symbolic or a positive integer.
• form and cond must be Function objects.
• DivisorSum is automatically simplified when n is a positive integer.
• DivisorSum is automatically simplified when form is a polynomial function.
Evaluate at positive integers:
Evaluate at positive integers:
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 Scope   (6)
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:
 Applications   (4)
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 :
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:
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