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An Achilles number is a number that is powerful but not a perfect power. A positive integer n is a powerful number if, for every prime factor p of n, p2 is also a divisor. In other words, every prime factor appears at least squared in the factorization. All Achilles numbers are powerful. However, not all powerful numbers are Achilles numbers. Powerful nummbers that can be represented as mk, where m and k are positive integers greater than 1 are not Acholies numbers.
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