Definition:Dirichlet Convolution/Definition 1

Definition

Let $f, g$ be arithmetic functions.

The Dirichlet convolution of $f$ and $g$ is the arithmetic function:

$\ds \map {\paren {f * g} } n = \sum_{d \mathop \divides n} \map f d \map g {\frac n d}$

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

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