Definition:Arithmetic Function

Definition
An arithmetic function or arithmetical function is a complex valued function defined on the strictly positive integers.

That is, a mapping:


 * $f: \Z_{>0} \to \C$

Examples
Examples of arithmetic functions include:


 * The Möbius function $\mu \left({n}\right)$


 * The Euler $\phi$ function $\phi \left({n}\right)$


 * The von Mangoldt function $\Lambda \left({n}\right)$

Also see

 * Definition:Dirichlet Series
 * Definition:Multiplicative Function
 * Definition:Dirichlet Convolution

Linguistic Note
In this context, the word arithmetic is pronounced with the stress on the first and third syllables: a-rith-me-tic, rather than on the second syllable: a-rith-me-tic.

This is because the word is being used in its adjectival form.