# $n$-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 $\displaystyle m=\prod_{j=0}^{n-1}{a_{j}}^{n+j}$.

Title $n$-full number NfullNumber 2013-03-22 16:02:51 2013-03-22 16:02:51 Wkbj79 (1863) Wkbj79 (1863) 6 Wkbj79 (1863) Definition msc 11A51 SquarefullNumber NFreeNumber cubefull cubefull number cube full cube full number cube-full cube-full number