Definition:Arithmetic Function

Definition
An arithmetic function or arithmetical function is a complex valued function defined on the natural numbers.

That is, a function:


 * $f: \N \to \C$

Examples
Common examples of arithmetic functions include:


 * The Möbius function $\mu(n)$


 * The Euler phi function $\phi(n)$


 * The von Mangoldt function $\Lambda(n)$

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.