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 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.