Definition:Multiplicative Arithmetic Function

Definition
Let $f : \N \to \C$ be an arithmetic function.

Then $f$ is multiplicative :
 * $m \perp n \implies \map f {m n} = \map f m \map f n$

where $m \perp n$ denotes that $m$ is coprime to $n$.

That is, a multiplicative function is one where the value of a product of two coprime numbers equals the product of the value of each one individually.

Also see

 * Definition:Additive Arithmetic Function
 * Definition:Completely Additive Function
 * Definition:Completely Multiplicative Function