# Achilles number

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: only those that cannot be represented as mk, where m and k are positive integers greater than 1. Achilles numbers were named by after Achilles, a hero of the Trojan war, who was also powerful but imperfect. Strong Achilles numbers are Achilles numbers whose Euler totients are also Achilles numbers. (Wikipedia).

What are Irrational Numbers? | Number System | Don't Memorise

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From playlist Number: Basic Arithmetic

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From playlist Algebra 1

212336448592654

From playlist everything

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From playlist MegaFavNumbers

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From playlist Concerning Education

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MegaFavNumbers My Mega Favorite Number ? 《百萬最數配》 你最愛哪個百萬大數？

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From playlist Classics & Ancient History

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From playlist MegaFavNumbers

## Related pages

Perfect power | Divisor | Powerful number