Jordan’s totient function

Let $p$ be a prime, $k$ and $n$ natural numbers. Then

 $J_{k}(n)=n^{k}\prod_{p|n}(1-p^{-k})$

where the product is over divisors of $n$.

This is a generalization of Euler’s Totient Function.

Title Jordan’s totient function JordansTotientFunction 2013-03-22 11:42:21 2013-03-22 11:42:21 akrowne (2) akrowne (2) 39 akrowne (2) Definition msc 11-00 msc 46M15 msc 18C15