-full number

The concept of a squarefull number can be generalized. Let $n \in \mathbb{Z}$ with $n>1$ . Then $m \in \mathbb{Z}$ is $n$ -full if, for every prime $p$ dividing $m$ , $p^n$ divides $m$ .

Note that $m$ is $n$ -full if and only if there exist $a_0, \dots, a_{n-1} \in \mathbb{Z}$ such that $\displaystyle m=\prod_{j=0}^{n-1} {a_j}^{n+j}$ .

-full number is owned by Warren Buck.