Arithmetic Function

In number theory, an arithmetic function, also called an arithmetical or number-theoretic function, is generally any function whose domain is the positive integers and whose range is a subset of the complex numbers, with some authors further requiring that it express some arithmetical property of its input. An example is the divisor function, whose value at a positive integer n is the number of divisors of n. Arithmetic functions are often highly irregular in their behavior, though some admit series expansions in terms of Ramanujan sums.