Geodesic
Sums of products of generalized Ramanujan sums
Journal of integer sequences, Tome 19 (2016) no. 2.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We consider weighted averages for the products $ t_{k_1}^{(1)}(j)\cdots t_{k_n}^{(n)}(j) $of generalized Ramanujan sums $ t_{k_i}^{(i)}(j)=\sum_{d\vert\gcd(k_{i},j)}f_{i}(d)g_{i} ({k_i}/{d})h_{i}({j}/{d}) $with any arithmetical functions $f_{i}, g_{i}$ and $h_{i} (i=1, \ldots, n),\ $ and derive formulas for several weighted averages with weights concerning completely multiplicative functions, completely additive functions, and others.
Classification : 11A25, 11B68
Keywords: arithmetical function, Ramanujan's sum, greatest common divisor 
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     author = {Ikeda, Soichi and Kiuchi, Isao and Matsuoka, Kaneaki},
     title = {Sums of products of generalized {Ramanujan} sums},
     journal = {Journal of integer sequences},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_2_a5/}
}
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Ikeda, Soichi; Kiuchi, Isao; Matsuoka, Kaneaki. Sums of products of generalized Ramanujan sums. Journal of integer sequences, Tome 19 (2016) no. 2. http://geodesic.mathdoc.fr/item/JIS_2016__19_2_a5/