Arithmetic function

In number theory, an arithmetic function is a function defined on the set of postive integers, usually with integer, real or complex values.

Classes of arithmetic function
Arithmetic functions which have some connexion with the additive or multiplicative structure of the integers are of particular interest in number theory. We define a function a(n) on positive integers to be
 * Totally multiplicative if $$a(mn) = a(m) a(n)$$ for all m and n.
 * Multiplicative if $$a(mn) = a(m) a(n)$$ whenever m and n are coprime.

Examples

 * Euler's totient function
 * Jordan's totient function