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An Achilles number is a powerful number that is not a perfect power. As such, Achilles numbers never have integers as square roots, cube roots, or any other root despite having a prime factorization entirely of powers. Named by Henry Bottomley for the Greek hero who was powerful but not without flaw. A few examples of Achilles numbers:

    72 = 23 ∗ 32 (this is also the smallest one)
    500 = 22 ∗ 53
    2,700 = 22 ∗ 33 ∗ 52
It's worth noting that not every powerful number whose prime factors have different exponents will be an Achilles number. If all of the exponents themselves have a common factor they will still be a perfect power. For instance:
    1,936 = 24 ∗ 112 = 442
    1,728 = 26 ∗ 33 = 123

The On-Line Encyclopedia of Integer Sequence list for Achilles numbers can be found here.

IRON NODER XIV: THE RETURN OF THE IRON NODER