Abstract:
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.
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