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:


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

Also see

 * Definition:Sequence, of which an arithmetic function is a particular instance


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

Examples

 * The Möbius function: $\map \mu n$


 * The Euler $\phi$ function: $\map \phi n$


 * The von Mangoldt function: $\map \Lambda n$