# 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.