The cubefree part of a positive integer is the quotient obtained by dividing it by its cubic
part. 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
 |
for 
, where 
is the real part of 
and 
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])
