V. V. Iudelevich

activity

20222026

most citedOn The Tree Structure of Natural Numbers, II

1 citations · 1 across the 6 of their papers we have counts for

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math.NT2023

Numbers of the form $k + f (k)$

Mikhail R. Gabdullin, Vitalii V. Iudelevich, Florian Luca

For a function $f : N \to N$ , let $$ N^+_f(x)=\{n\leq x: n=k+f(k) \mbox{ for some } k\}. $$ Let $τ (n) = \sum_{d ∣ n} 1$ be the divisor function, $ω (n) = \sum_{p ∣ n} 1$ b…

math.NT2023

Karatsuba's divisor problem and related questions

Mikhail R. Gabdullin, Vitalii V. Iudelevich, Sergei V. Konyagin

We prove that $p \leq x \sum \frac{1}{τ ( p - 1 )} ≍ \frac{x}{( lo g x ) ^{3/2}}, n \leq x \sum \frac{1}{τ ( n ^{2} + 1 )} ≍ \frac{x}{( lo g x ) ^{1/2}},$ where $τ(n)=\s…

math.NT2023

On the Karatsuba divisor problem

Vitalii V. Iudelevich

We obtain an upper bound for the sum $Φ_{a} (x) = \sum_{p \leq x} 1/ (τ (p + a))$ , where $τ (n)$ is the divisor function, $a \geq 1$ is a fixed integer, and $p$ run through primes up to $x$ .

Numbers of the form k+f(k)

Karatsuba's divisor problem and related questions

On the Karatsuba divisor problem

Numbers of the form $k + f (k)$