On Karatsuba's Problem Concerning the Divisor Function $τ(n)$

Details On Karatsuba's Problem Concerning the Divisor Function $τ(n)$ On Karatsuba's Problem Concerning the Divisor Function $τ(n)$

2010-11-05

arxiv.org/abs/1011.1391v1

Mathematics

Number Theory

32 pages

Scientific paper

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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