Geodesic
On Numbers Not Representable as $n+w(n)$
Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 392-404.

Voir la notice de l'article provenant de la source Math-Net.Ru

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, additive function.
Mots-clés : Perron's formula 
@article{MZM_2023_113_3_a5,
     author = {P. A. Kucheryavyi},
     title = {On {Numbers} {Not} {Representable} as $n+w(n)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {392--404},
     publisher = {mathdoc},
     volume = {113},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a5/}
}
TY  - JOUR
AU  - P. A. Kucheryavyi
TI  - On Numbers Not Representable as $n+w(n)$
JO  - Matematičeskie zametki
PY  - 2023
SP  - 392
EP  - 404
VL  - 113
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a5/
LA  - ru
ID  - MZM_2023_113_3_a5
ER  - 
%0 Journal Article
%A P. A. Kucheryavyi
%T On Numbers Not Representable as $n+w(n)$
%J Matematičeskie zametki
%D 2023
%P 392-404
%V 113
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a5/
%G ru
%F MZM_2023_113_3_a5
P. A. Kucheryavyi. On Numbers Not Representable as $n+w(n)$. Matematičeskie zametki, Tome 113 (2023) no. 3, pp. 392-404. http://geodesic.mathdoc.fr/item/MZM_2023_113_3_a5/

[1] M. E. Changa, “O chislakh, kolichestvo prostykh delitelei kotorykh prinadlezhit zadannomu klassu vychetov”, Izv. RAN Ser. matem., 83:1 (2019), 192–202 | DOI | MR

[2] M. E. Changa, Metody analiticheskoi teorii chisel, MTsNMO, 2019

[3] A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, 2-e izd., Nauka, M., 1983 | MR

[4] R. C. Baker, G. Harman, J. Pintz, “The difference between consecutive primes. II”, Proc. London Math. Soc., 83:3 (2001), 532–562 | DOI | MR | Zbl

[5] P. Erdős, A. Sárkőzy, C. Pomerance, “On locally repeated values of certain arithmetic functions. I”, J. Number Theory, 21:3 (1985), 319–332 | DOI | MR