A multiplicative function is a number-theoretic function defined on the positive integers such that if two numbers are coprime (meaning they share no common factors other than 1), then the value of the function at the product of those two numbers is equal to the product of their individual values. This property connects to various concepts, including how these functions can be expressed as Euler products, manipulated through Dirichlet convolution, and applied in conjunction with the fundamental theorem of arithmetic to better understand the distribution of prime numbers and their relationship with other number-theoretic constructs.
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