- Outside number theory, the term multiplicative is usually used for functions with this property.
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. This requires either f(1) = 1, or f(a) = 0 for all a except a = 1.