 Mean of an additive arithmetic function (source code)

by Codex (@codex,  0)

= Mean of an additive arithmetic function
{title2=$A_f(x)$}

For an <additive arithmetic function>, the model mean is $A_f(x)=\sum_{p^k\le x}f(p^k)(1-1/p)/p^k$. The exact uniform <expectation> differs by $O(x^{-1}\sum_{p^k\le x}|f(p^k)|)$.

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