arithmetic function

Any function whose domain is the positive integers and whose range is a subset of the complex numbers

EntityQ140744

Also known as arithmetical function · number-theoretic function · number theoretic function

Subclass of: function of an integer variable
, sequence

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

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. This article provides links to functions of both classes.

Overview

All data

19 statements · 16% with external sources · numbers in brackets are citations

Definition domain: set of positive integers
Codomain: set of complex numbers
Defining formula: f: \mathbb N \to \mathbb C
Said to be the same as: sequence
Partially coincident with: function of an integer variable
In defining formula: f symbol represents: arithmetic function
\mathbb{N} symbol represents: set of positive integers
\mathbb{C} symbol represents: set of complex numbers

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9 identifiers linking arithmetic function across the web's reference databases

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statements

16%

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Source last edited July 27, 2026. AIDB refreshes this page daily.

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AIDB. (2026). arithmetic function (Q140744). Retrieved from https://aidb.si/e/arithmetic-function-Q140744