A positive integer $n$ is called square-full or powerfull if $p^2|n$ for every factor $p$ of $n$ for every prime factor $p$.
I need to show that if $n$ is square-full show so it can be written in the form $n=a^2b^3$ for $a,b$ positive integer.
I looked in wikipedia but the proof was too complicated... is there any easy way to prove this?