On numbers not representable as $n + w(n)$

Petr Kucheriaviy

On numbers not representable as $n + w(n)$

Number Theory 2022-11-29 v3

Authors: Petr Kucheriaviy

Abstract

Let $w(n)$ be an additive non-negative integer-valued arithmetic function which is equal to $1$ on primes. We study the distribution of $n + w(n)$ $\pmod p$ and give a lower bound for the density of the set of numbers which are not representable as $n + w(n)$ .

Keywords

prime number theory prime numbers additive number theory

Cite

@article{arxiv.2203.12006,
  title  = {On numbers not representable as $n + w(n)$},
  author = {Petr Kucheriaviy},
  journal= {arXiv preprint arXiv:2203.12006},
  year   = {2022}
}

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