n-free number

The concept of a squarefreeMathworldPlanetmath number can be generalized. Let n with n>1. Then m is n-free if, for any prime p, pn does not divide m.

Let S denote the set of all squarefree natural numbersMathworldPlanetmath. Note that, for any n and any positive n-free integer m, there exists a unique (a1,,an-1)Sn-1 with gcd(ai,aj)=1 for ij such that m=j=1n-1ajj.

Title n-free number
Canonical name NfreeNumber
Date of creation 2013-03-22 16:02:22
Last modified on 2013-03-22 16:02:22
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 6
Author Wkbj79 (1863)
Entry type Definition
Classification msc 11A51
Related topic SquareFreeNumber
Related topic NFullNumber
Defines cubefreeMathworldPlanetmath
Defines cubefree number
Defines cube free
Defines cube free number
Defines cube-free
Defines cube-free number