sum-of-divisors transform

The transformation of a sequence a_1, a_2, ... with a_n = sum_(d|n) b_d into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n = sum_(d|n) μ(n/d) a_d. The transformation of b_n to a_n is sometimes called the sum-of-divisors transform.

binomial transform | Dirichlet generating function | divisor function | Euler transform | Lambert series | Möbius inversion formula | Möbius transformation | Stirling transform