Rough Integers with A Divisor in A Given Interval

Research output: Contribution to journalArticle


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)
JournalJournal of the Australian Mathematical Society
StateAccepted/In press - Jan 1 2019


  • 11N25
  • 2010 Mathematics subject classification
  • 62G30

ASJC Scopus subject areas

  • Mathematics(all)

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