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])
