A Hardy–Ramanujan-type inequality for shifted primes and sifted sets

Research output: Contribution to journalArticlepeer-review

Abstract

We establish an analog of the Hardy–Ramanujan inequality for counting members of sifted sets with a given number of distinct prime factors. In particular, we establish a bound for the number of shifted primes p + a below x with k distinct prime factors, uniformly for all positive integers k.

Original languageEnglish (US)
Pages (from-to)323-329
Number of pages7
JournalLithuanian Mathematical Journal
Volume61
Issue number3
DOIs
StatePublished - Jul 2021

Keywords

  • Hardy–Ramanujan inequality
  • shifted primes
  • sieves

ASJC Scopus subject areas

  • General Mathematics

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