arithmetical function

An arithmetic function is a function f(n) defined for all n element N, usually taken to be complex-valued, so that f:N->C. An alternative definition of arithmetic function is a function ψ(n) such that ψ(n + m) = ψ(ψ(n) + ψ(m)) and ψ(n m) = ψ(ψ(n) ψ(m)) (Atanassov 1985; Trott 2004, p. 28).

integer function | number theoretic function