Definition:Logarithmic Mean Value
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Definition
Let $f: \N \to \C$ be an arithmetic function.
The logarithmic mean value of $f$ is the limit:
- $\map L f = \ds \lim_{x \mathop \to \infty} \frac 1 {\ln x} \sum_{n \mathop \le x} \frac {\map f n} n$
if it exists.