Geodesic
On the Karatsuba divisor problem
Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 992-1019

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We obtain an upper bound for the sum $$\Phi_a(x) = \sum_{p\leqslant x}\frac{1}{\tau(p+a)},$$ where $\tau(n)$ is the divisor function, $a\geqslant 1$ is a fixed integer, and $p$ runs through primes up to $x$.
Keywords: divisor function, shifted primes. 
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     author = {V. V. Iudelevich},
     title = {On the {Karatsuba} divisor problem},
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V. V. Iudelevich. On the Karatsuba divisor problem. Izvestiya. Mathematics , Tome 86 (2022) no. 5, pp. 992-1019. http://geodesic.mathdoc.fr/item/IM2_2022_86_5_a8/