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The most important arithmetic functions are the [[additive function|additive]] and the [[multiplicative function|multiplicative]] ones. An important operation on arithmetic functions is the [[Dirichlet convolution]]. Arithmetic functions may be studied with [[Bell series]].
Formally, an '''arithmetic function''' is simply a sequence, with real or complex values. A sequence is, of course, a [[function]] on the set of [[natural number]]s (i.e. [[positive]] [[integer]]s). To emphasize that we are thinking of them as functions, we shall usually use notation like ''a(n)'', rather than ''a<sub>n</sub>'', for the value corresponding to the integer ''n''. The term arithmetic function is used especially when ''a(n)'' is defined using number-theoretic properties in some way. A large part of number theory consists, in one way or another, of the study of these functions.
==Examples==
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