A Sum of Gcd’s over Friable Numbers

Abstract:

We study the function

$\begin{displaymath}g(n,y):=\sum_{\substack{i \leq n\\ P(i)\leq y}}\gcd(i,n),\end{displaymath}$

where P(n) denotes the largest prime factor of n, and we derive some estimates for its summatory function.

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(Concerned with sequence A018804.)

Received September 14 2015; revised version received February 8 2016. Published in Journal of Integer Sequences, April 5 2016.