Geodesic
On the Mean Values of the Function~$\tau_k(n)$ in Sequences of Natural Numbers
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 454-463

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We obtain an asymptotic formula for the mean value of the function $\tau_k(n)$, which is the number of solutions of the equation $x_1\dotsb x_k=n$ in natural numbers $x_1,\dots,x_k$, in some special sequences of natural numbers.
Keywords: sequence of natural numbers, trigonometric sum, number system of base $q$, complex-valued function, inequality of the large sieve. 
@article{MZM_2011_90_3_a10,
     author = {K. M. Eminyan},
     title = {On the {Mean} {Values} of the {Function~}$\tau_k(n)$ in {Sequences} of {Natural} {Numbers}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {454--463},
     publisher = {mathdoc},
     volume = {90},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a10/}
}
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K. M. Eminyan. On the Mean Values of the Function~$\tau_k(n)$ in Sequences of Natural Numbers. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 454-463. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a10/