Definition:Arithmetic Function

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

That is, a mapping:

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

Also see


Linguistic Note

In the context of an arithmetic function, 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.