# radical of an integer

Given a natural number $n$, let $n=p_{1}^{{\alpha}_{1}}\cdots p_{k}^{{\alpha}_{k}}$ be its unique factorization as a product of distinct prime powers. Define the of $n$, denoted $\mbox{rad}(n)$, to be the product $p_{1}\cdots p_{k}$. 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