##### Wiktionary

**arithmetic function**

n. (context analysis English) Any function that is defined for all positive integers, and has values that are either real or complex.

##### Wikipedia

**Arithmetic function**

In number theory, an **arithmetic**, **arithmetical**, or **number-theoretic function** is a real or complex valued function *f*(*n*) defined on the set of natural numbers (i.e., positive integers) that "expresses some arithmetical property of *n*".

An example of an arithmetic function is the divisor function whose value at a positive integer *n* is equal to the number of divisors of *n*.

There is a larger class of number-theoretic functions that do not fit the above definition, e.g. the prime-counting functions. This article provides links to functions of both classes.