Except for , , , and , the functions in §27.2 are multiplicative, which means and
If is multiplicative, then the values for are determined by the values at the prime powers. Specifically, if is factored as in (27.2.1), then
Related multiplicative properties are
A function is completely multiplicative if and
Examples are and , and the Dirichlet characters, defined in §27.8.
If is completely multiplicative, then (27.3.2) becomes