\begin{definition}[Definition:Dirichlet Convolution/Definition 2]
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 $a b = n$.
Category:Definitions/Dirichlet Convolution
\end{definition}