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)
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:
The On-Line Encyclopedia of Integer Sequence list for Achilles numbers can be found here.
IRON NODER XIV: THE RETURN OF THE IRON NODER