# Average order of an arithmetic function

In mathematics, in the field of number theory, the average order of an arithmetic function is some simpler or better-understood function which takes the same values "on average".

Let f be a function on the natural numbers. We say that the average order of f is g if

$\sum_{n \le x} f(n) \sim \sum_{n \le x} g(n)$

as x tends to infinity.

It is conventional to assume that the approximating function g is continuous and monotone.