Arithmetic function

In number theory, an arithmetic, arithmetical, or number-theoretic function is generally any function whose domain is the set of positive integers and whose range is a subset of the complex numbers. Hardy & Wright include in their definition the requirement that an arithmetical function "expresses some arithmetical property of n". There is a larger class of number-theoretic functions that do not fit this definition, for example, the prime-counting functions.

Extends: [Arithmetic functions](https://wikipedia.org.ai/Arithmetic functions), [Functions and mappings](https://wikipedia.org.ai/Functions and mappings)