\begin{definition}[Definition:Dirichlet Convolution/Definition 1]
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 $n$.
Category:Definitions/Dirichlet Convolution
\end{definition}