An integer m such that if p|m, then p^2|m, is called a powerful number. There are an infinite number of powerful numbers, and the first few are 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, ... (OEIS A001694). Powerful numbers are always of the form a^2 b^3 for a, b>=1. The numbers of powerful numbers <=10, 10^2, 10^3, ... are given by 4, 14, 54, 185, 619, 2027, 6553, 21044, 67231, 214122, 680330, 2158391, ... (OEIS A118896).
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