Geodesic
The gcd-sum function
Journal of integer sequences, Tome 4 (2001) no. 2
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.
Classification : 11A05, 11N56, 11N37
Mots-clés : gcd-sum, arithmetic function, asymptotic estimates, lattice point counting, polynomial growth, Dirichlet series, Riemann zeta-function 
@article{JIS_2001__4_2_a1,
     author = {Broughan,  Kevin A.},
     title = {The gcd-sum function},
     journal = {Journal of integer sequences},
     year = {2001},
     volume = {4},
     number = {2},
     zbl = {1004.11005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2001__4_2_a1/}
}
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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/