In number theory, an arithmetic function (or number-theoretic function) f(n) is a function defined for all positive integers and having values in the complex numbers (f : N → C).
Another definition of arithmetic function is a function with properties:
- Ψ(m+n) = Ψ[Ψ(m)+Ψ(n)]
- Ψ(m,n) = Ψ[Ψ(m)Ψ(n)]
The most important arithmetic functions are the multiplicative ones.
Arithmetic function should not be confused with a function sometimes called arithmetical function.