Geodesic
Mean values of a class of arithmetical functions
Journal of integer sequences, Tome 14 (2011) no. 6
In this paper we consider a class of functions $ \mathcal {U}$ of arithmetical functions which include $ \tilde{P}(n)/n$, where $ \tilde{P}(n):=n \prod_{p\vert n}(2-\frac{1}{p})$. For any given $ U\in\mathcal {U}$, we obtain the asymptotic formula for $ \sum_{n\leq x}U(n)$, which improves a result of De Koninck and Kátai.
Keywords: gcd-sum function, regular integers modulo n, Riemann hypothesis, short interval result 
@article{JIS_2011__14_6_a4,
     author = {Zhang,  Deyu and Zhai,  Wenguang},
     title = {Mean values of a class of arithmetical functions},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {6},
     zbl = {1266.11105},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_6_a4/}
}
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Zhang,  Deyu; Zhai,  Wenguang. Mean values of a class of arithmetical functions. Journal of integer sequences, Tome 14 (2011) no. 6. http://geodesic.mathdoc.fr/item/JIS_2011__14_6_a4/