Definition:Dirichlet Convolution/Definition 2

Definition
Let $f, g$ be arithmetic functions.

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

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