Journal of Integer Sequences, Vol. 19 (2016), Article 16.3.2

A Sum of Gcd’s over Friable Numbers

Julian Ransford
Département de Mathématiques et de Statistique
Université Laval
Québec, PQ G1V 0A6


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.

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