Additive function

In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime, the function of the product is the sum of the functions: In number theory, an additive function is an arithmetic function f(n) of the positive integer n such that whenever a and b are coprime, the function of the product is the sum of the functions: An additive function f(n) is said to be completely additive if f(ab) = f(a) + f(b) holds for all positive integers a and b, even when they are not co-prime. Totally additive is also used in this sense by analogy with totally multiplicative functions. If f is a completely additive function then f(1) = 0.