Definition:Dirichlet Convolution/Definition 1

Definition
Let $f, g$ be arithmetic functions.

The Dirichlet convolution of $f$ and $g$ is the arithmetic function:
 * $\ds \map {\paren {f * g} } n = \sum_{d \mathop \divides n} \map f d \map g {\frac n d}$

where the summation runs over the set of positive divisors $d$ of $n$.