Geodesic
The gcd-sum function
Journal of integer sequences, Tome 4 (2001) no. 2.

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

Summary: The gcd-sum is an arithmetic function defined as the sum of the gcd's of the first n integers with n: $g(n) = sum_{i=1..n}$ (i, n). The function arises in deriving asymptotic estimates for a lattice point counting problem. The function is multiplicative, and has polynomial growth. Its Dirichlet series has a compact representation in terms of the Riemann zeta function. Asymptotic forms for values of partial sums of the Dirichlet series at real values are derived, including estimates for error terms. 
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     author = {Broughan, Kevin A.},
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Broughan, Kevin A. The gcd-sum function. Journal of integer sequences, Tome 4 (2001) no. 2. http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a1/