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

collaborators

8 papers

math.NT2026

Distinct exponents in the prime factorization

Mikhail R. Gabdullin, Vitalii V. Iudelevich

Following Erdős (1982) and Sanna (2019), we study the arithmetic function $h (n)$ , which is defined to be the number of distinct exponents in the prime factorization of a positive i…

math.NT2025

Generalization of the Ford-Zaharescu Theorem

Elizaveta D. Iudelevich, Vitalii V. Iudelevich

We derive an asymptotic formula for the sum $H = 0 < γ_{k} ⩽ T, 1 ⩽ k ⩽ m \sum h (a_{1} γ_{1} + a_{2} γ_{2} + \dots + a_{m} γ_{m}),$ where $a_{1}, a_{2}, \dots, a_{m}$ are integers…

math.NT2025

On the sum-of-squares function

Vitalii V. Iudelevich

In this paper, we derive the following asymptotic formula $\sum^{'}_{n ⩽ x} \frac{r ( n )}{r ( n + 1 )} = x (ln x)^{- 3/4} (c + o (1)), x \to + \infty,$ where $r (n)$ is…

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 $x$ .

math.NT2022★ 1 cited

On The Tree Structure of Natural Numbers, II

Vitalii V. Iudelevich

Each natural number can be associated with some tree graph. Namely, a natural number $n$ can be factorized as $n = p_{1}^{α_{1}} \dots p_{k}^{α_{k}},$ where $p_{i}$ are distinct prime num…

math.NT2022

Numbers of the form $k f (k)$

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

For a function $f : N \to N$ , define $N^{\times}_{f}(x)=\#\{n\leq x: n=kf(k) \mbox{ for some $k$} \}$. Let $τ (n) = \sum_{d ∣ n} 1$ be the divisor function, $ω(n)=\su…

Distinct exponents in the prime factorization

Generalization of the Ford-Zaharescu Theorem

On the sum-of-squares function

Numbers of the form k+f(k)

Karatsuba's divisor problem and related questions

On the Karatsuba divisor problem

On The Tree Structure of Natural Numbers, II

Numbers of the form kf(k)

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

Numbers of the form $k f (k)$