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A number is squareful, also called Nonsquarefree, if it contains at least one Square in its prime factorization. Such a number is also called Squareful. The first few are 4, 8, 9, 12, 16, 18, 20, 24, 25, ... (Sloane's A013929). The greatest multiple prime factors for the squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 3, ... (Sloane's A046028). The least multiple prime factors for squareful integers are 2, 2, 3, 2, 2, 3, 2, 2, 5, 3, 2, 2, 2, ... (Sloane's A046027).
See also Greatest Prime Factor, Least Prime Factor, Smarandache Near-to-Primorial Function, Squarefree
References
Sloane, N. J. A. Sequences
A013929,
A046027, and
A046028
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html.