Cubefree Part

The cubefree part is that part of a positive integer left after all cubic factors are divided out. For example, the cubefree part of  is 3. For , 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

where  is the Riemann zeta function.

The cubefree part function can be implemented in the Wolfram Language as:

  CubefreePart[n_Integer?Positive] :=
    Times @@ Power @@@ ({#[[1]], Mod[#[[2]], 3]}& /@
      FactorInteger[n])

REFERENCES:

Sloane, N. J. A. Sequence A050985 in "The On-Line Encyclopedia of Integer Sequences."