 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 whenever
"a" and "b" are coprime, then

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.Some multiplicative functions are defined to make formulas easier to write