 Powerful number

A positive integer is squarefull when every prime dividing it also divides it to at least the second power. Thus $n$ is not squarefull as soon as some prime $p$ satisfies $p\mid n$ but $p^2\nmid n$.

A **powerful number** is a positive integer \( n \) such that for every prime \( p \) that divides \( n \), \( p^2 \) also divides \( n \). In other words, if a prime number appears in the factorization of a powerful number, it must appear with an exponent of at least 2.