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 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


where zeta(s) 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]}& /@

See also

Cubefree, Cubic Part, Squarefree Part

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

Referenced on Wolfram|Alpha

Cubefree Part

Cite this as:

Weisstein, Eric W. "Cubefree Part." From MathWorld--A Wolfram Web Resource.

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