Liubomir Chiriac Portland State University, Fariborz Maseeh Department of Mathematics and Statistics, Portland, OR 97201, USA

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In this paper we study the sum px τ(np), where τ(n) denotes the number of divisors of n, and {np} is a sequence of integers indexed by primes. Under certain assumptions we show that the aforementioned sum is  x as x . As an application, we consider the case where the sequence is given by the Fourier coefficients of a modular form.

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