$n$-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 $a_0,\mathrm{\dots },a_{n-1}\in \mathbb{Z}$ such that $m={\displaystyle \prod _{j=0}^{n-1}}a_j{}^{n+j}$.

Title	$n$-full number
Canonical name	NfullNumber
Date of creation	2013-03-22 16:02:51
Last modified on	2013-03-22 16:02:51
Owner	Wkbj79 (1863)
Last modified by	Wkbj79 (1863)
Numerical id	6
Author	Wkbj79 (1863)
Entry type	Definition
Classification	msc 11A51
Related topic	SquarefullNumber
Related topic	NFreeNumber
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