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On Karatsuba's Problem Concerning the Divisor Function $τ(n)$
Published 5 Nov 2010 in math.NT | (1011.1391v1)
Abstract: We study an asymptotic behavior of the sum $\sum\limits_{n\le x}\frac{\D \tau(n)}{\D \tau(n+a)}$. Here $\tau(n)$ denotes the number of divisors of $n$ and $a\ge 1$ is a fixed integer.
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