Arithmetic function
From Citizendium
In number theory, an arithmetic function is a function defined on the set of positive 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.
Multiplicative functions
We define a function a(n) on positive integers to be
- Totally multiplicative if for all m and n.
- Multiplicative if whenever m and n are coprime.
The Dirichlet convolution of two arithmetic function a(n) and b(n) is defined as
If a and b are multiplicative, so is their convolution.