Abstract
We shall consider some formulas for weighted averages of the generalized Ramanujan sum $\sum_{d|\gcd(k,n)}f(d)g\left({k}/{d}\right)h\left({n}/{d}\right)$ for any arithmetical functions $f,\ g$ and $h$, with the weights concerning completely multiplicative functions, completely additive functions and others.
Citation
Isao KIUCHI. "On Sums of Averages of Generalized Ramanujan Sums." Tokyo J. Math. 40 (1) 255 - 275, June 2017. https://doi.org/10.3836/tjm/1502179227