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
Canonical name	JordansTotientFunction
Date of creation	2013-03-22 11:42:21
Last modified on	2013-03-22 11:42:21
Owner	akrowne (2)
Last modified by	akrowne (2)
Numerical id	39
Author	akrowne (2)
Entry type	Definition
Classification	msc 11-00
Classification	msc 46M15
Classification	msc 18C15