Definition:Dirichlet Convolution/Definition 1

Definition
Let $f, g$ be arithmetic functions.

The Dirichlet convolution of $f$ and $g$ is the arithmetic function:
 * $\displaystyle \left({f * g}\right) \left({n}\right) := \sum_{d \mathop \backslash n} f \left({d}\right) g \left({\frac n d}\right)$

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