ROUGH INTEGERS with A DIVISOR in AA GIVENA INTERVAL

Research output: Contribution to journalArticlepeer-review

Abstract

We determine, up to multiplicative constants, the number of integers that have a divisor in and no prime factor. Our estimate is uniform in. We apply this to determine the order of the number of distinct integers in the multiplication table, which are free of prime factors, and the number of distinct fractions of the form with and.

Original languageEnglish (US)
Pages (from-to)17-36
Number of pages20
JournalJournal of the Australian Mathematical Society
Volume111
Issue number1
DOIs
StatePublished - Aug 2021

Keywords

  • 11N25
  • 2010 Mathematics subject classification
  • 62G30
  • divisors
  • Farey fractions.

ASJC Scopus subject areas

  • General Mathematics

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