Definition:Dirichlet Convolution/Definition 2

Definition
Let $f, g$ be arithmetic functions.

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

where the summation runs over all pairs of positive integers $\tuple {a, b}$ with $a b = n$.