Additive function

Function that can be written as a sum over prime factors

In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to the product ab is the sum of the values of the function applied to a and b: f ( a b) = f ( a) + f ( b) . {\displaystyle f(ab)=f(a)+f(b).} It follows that for any additive function, f ( 1) = 0 {\displaystyle f(1)=0} .

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