# Arithmetic function

In number theory, an arithmetic, arithmetical, or number-theoretic function is for most authors any function f(n) whose domain is the 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". 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. Many of the functions mentioned in this article have expansions as series involving these sums; see the article Ramanujan's sum for examples.

## Words

This table shows the example usage of word lists for keywords extraction from the text above.

Word | Word Frequency | Number of Articles | Relevance |
---|---|---|---|

arithmetical | 4 | 80 | 0.328 |

function | 7 | 22122 | 0.284 |

number-theoretic | 3 | 17 | 0.28 |

arithmetic | 4 | 1443 | 0.243 |

functions | 5 | 18173 | 0.21 |