Definition:Logarithmic Mean Value

Definition
Let $f:\N\to\C$ be an arithmetic function.

The logarithmic mean value of $f$ is the limit:
 * $L(f) = \displaystyle \lim_{x\to\infty}\frac 1{\log x}\sum_{n\leq x} \frac{f(n)}n$

if it exists.

Also see

 * Definition:Ordinary Mean Value
 * Existence of Ordinary Mean Value Implies Existence of Logarithmic Mean Value