A positive integer 
is 
th
powerfree if there is no number 
such that 
(
divides 
),
i.e., there are no 
th
powers or higher in the prime factorization
of 
. A number which is free of all powers
is therefore squarefree.
Powerfree
See also
Biquadratefree, Cubefree, Prime Number, SquarefreeExplore with Wolfram|Alpha
References
Baake, M.; Moody, R. V.; and Pleasants, P. A. B. "Diffraction from Visible Lattice Points and
th Power Free Integers." 19 Jun 1999. http://arxiv.org/abs/math.MG/9906132.Referenced on Wolfram|Alpha
PowerfreeCite this as:
Weisstein, Eric W. "Powerfree." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Powerfree.html