This article is cited in 1 paper

On Numbers Not Representable as $n+w(n)$

P. A. Kucheryavyi

Faculty of Mathematics, National Research University Higher School of Economics, Moscow

Abstract: Let $w(n)$ be an additive nonnegative integer-valued arithmetic function equal to $1$ on primes. We study the distribution of $n+w(n)$ modulo a prime $p$ and give a lower bound for the density of numbers not representable as $n+w(n)$.

Keywords: number of prime divisors, Perron's formula, additive function.

UDC: 511

PACS: 02.10.De

MSC: 11M99

Received: 08.09.2022
Revised: 05.10.2022

DOI: 10.4213/mzm13718

 English version: Mathematical Notes, 2023, 113:3, 384–395

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