Achilles number

[1] A positive integer n is a powerful number if, for every prime factor p of n, p2 is also a divisor.

Achilles numbers were named by Henry Bottomley after Achilles, a hero of the Trojan War, who was also powerful but imperfect.

However, 108 cannot be represented as mk, where m and k are positive integers greater than 1, so 108 is an Achilles number.

The integer 360 is not an Achilles number because it is not powerful.

It is a powerful number, because not only are 2 and 7 its only prime factors, but also 22 = 4 and 72 = 49 are divisors of it.