: Mathématiques: multiplicative function

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multiplicative function

In number theory, a multiplicative function is an arithmetic function f(n) of a positive integer n with the property that f(1) = 1 and ${\\displaystyle f(ab)=f(a)f(b)}$ whenever a and b are coprime. An arithmetic function f(n) is said to be completely multiplicative (or totally multiplicative) if f(1) = 1 and f(ab) = f(a)f(b) holds for all positive integers a and b, even when they are not coprime.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Multiplicative_function)

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