Definition
If ƒ and g are two arithmetic functions (i.e. functions from the positive integers to the complex numbers), one defines a new arithmetic function ƒ * g, the Dirichlet convolution of ƒ and g, by
where the sum extends over all positive divisors d of n, or equivalently over all pairs (a, b) of positive integers whose product is n.
Read more about this topic: Dirichlet Convolution
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