Powerful-squarefree coprime decomposition
= Powerful-squarefree coprime decomposition
Every positive integer has a unique factorization $n=as$ with $a$ <powerful>, $s$ <squarefree>, and $\gcd(a,s)=1$: assign each prime power of exponent at least two to $a$, and each prime of exponent one to $s$. In general $s$ differs from the <squarefree part>, which instead retains every prime of odd exponent.