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Dirichlet convolution
In mathematics, the Dirichlet convolution is a binary operation defined for arithmetic functions; it is important in number theory. It was developed by Peter Gustav Lejeune Dirichlet, a German mathematician.
==Definition==
If ''f'' and ''g'' are two arithmetic functions (i.e. functions from the positive integers to the complex numbers), one defines a new arithmetic function , the ''Dirichlet convolution'' of ''f'' and ''g'', by
:
where the sum extends over all positive divisors ''d'' of ''n'', or equivalently over all distinct pairs of positive integers whose product is ''n''.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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