# §27.3 Multiplicative Properties

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

In particular,

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