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 primepowers. Define the radical of $n$ , denoted $\mbox{rad}(n)$ , to be the product $p_1 \cdots p_k$ . The radical of a square-free number is itself.
