Squarefree Part

That part of a positive integer left after all square factors are divided out. For example, the squarefree part of  is 6, since . For , 2, ..., the first few are 1, 2, 3, 1, 5, 6, 7, 2, 1, 10, ... (OEIS A007913). The squarefree part function can be implemented in the Wolfram Language as

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

REFERENCES:

Atanassov, K. "On the 22nd, 23rd, and the 24th Smarandache Problems. Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria 5, 80-82, 1999.

Atanassov, K. On Some of the Smarandache's Problems. Lupton, AZ: American Research Press, pp. 16-21, 1999.

Sloane, N. J. A. Sequence A007913 in "The On-Line Encyclopedia of Integer Sequences."

Smarandache, F. Only Problems, Not Solutions!, 4th ed. Phoenix, AZ: Xiquan, 1993.