# Dedekind psi-function

From Number

This article defines an arithmetic function or number-theoretic function: a function from the natural numbers to a ring (usually, the ring of integers, rational numbers, real numbers, or complex numbers).

View a complete list of arithmetic functions

## Definition

The Dedekind psi-function is an arithmetic function that sends any natural number to the number:

where the product is over all primes dividing .

## Relation with other arithmetic functions

- Euler phi-function has a similar expression to the Dedekind psi-function, except that the expression is rather than .