radical of an integer

Given a natural number $n$, let $n=p_1^{{\alpha }_1}\mathrm{\cdots }{p}_k^{{\alpha }_k}$ be its unique factorization as a product of distinct prime powers. Define the of $n$, denoted $\text{rad}(n)$, to be the product $p_1\mathrm{\cdots }{p}_k$. The radical of a square-free number is itself.

Title	radical of an integer
Canonical name	RadicalOfAnInteger
Date of creation	2013-03-22 11:45:21
Last modified on	2013-03-22 11:45:21
Owner	KimJ (5)
Last modified by	KimJ (5)
Numerical id	12
Author	KimJ (5)
Entry type	Definition
Classification	msc 13A10
Classification	msc 81-00
Classification	msc 18-00
Synonym	square-free part
Related topic	RadicalOfAnIdeal
Related topic	PowerOfAnInteger
Defines	radical