Karatsuba's divisor problem and related questions

M. R. Gabdullin,S. Konyagin, V. V. Iudelevich

SBORNIK MATHEMATICS（2023）

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摘要

We prove that Sigma(p <= x)1/tau (p - 1) (sic) x/(log x)(3/2) and Sigma(n <= x) 1/tau(n(2) + 1) (sic) x/(log x)(1/2), where tau(n) = Sigma(d vertical bar n) 1 is the number of divisors of n, and the first sum is taken over prime numbers.

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关键词

divisor function,sums of values of functions,shifted primes and squares

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