The cubefree part is that part of a positive integer left after all cubic factors are divided out. For example, the cubefree part of 24 = 2^3·3 is 3. For n = 1, 2, ..., the first few are 1, 2, 3, 4, 5, 6, 7, 1, 9, 10, 11, 12, 13, 14, 15, 2, ... (OEIS A050985). The sequence of cubefree parts of positive integers has Dirichlet generating function f(s) = (ζ(3s) ζ(s - 1))/(ζ(3s - 3)), where ζ(s) is the Riemann zeta function.

cubefree | cubic part | squarefree part