Geodesic
A survey of gcd-sum functions
Journal of integer sequences, Tome 13 (2010) no. 8
We survey properties of the gcd-sum function and of its analogs. As new results, we establish asymptotic formulae with remainder terms for the quadratic moment and the reciprocal of the gcd-sum function and for the function defined by the harmonic mean of the gcd's.
Classification : 11A25, 11N37
Keywords: gcd-sum function, Euler's arithmetical function, divisor function, unitary divisor, exponential divisor, regular integer (mod n), average order 
@article{JIS_2010__13_8_a4,
     author = {T\'oth,  L\'aszl\'o},
     title = {A survey of gcd-sum functions},
     journal = {Journal of integer sequences},
     year = {2010},
     volume = {13},
     number = {8},
     zbl = {1206.11118},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a4/}
}
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Tóth,  László. A survey of gcd-sum functions. Journal of integer sequences, Tome 13 (2010) no. 8. http://geodesic.mathdoc.fr/item/JIS_2010__13_8_a4/