Uniform distribution of some ratios involving the number of prime and integer divisors

Florian Luca, Igor E. Shparlinski

Research output: Contribution to journalArticle

Abstract

We show that the fractional parts of the ratios n/ω(n), n/aω(n), n/τ(n) and n/aτ(n), where a ≥ 2 is a fixed integer and, as usual, ω(n) and τ(n) denote the number of prime divisors and the total number of divisors of n > 1, respectively, are uniformly distributed in the unit interval [0, 1]. This complements results of several authors about the scarcity of integral values taken by the above fractions.
Original languageEnglish
Pages (from-to)15-26
Number of pages12
JournalUniform distribution theory
Volume1
Issue number1
Publication statusPublished - 2006

Keywords

  • sequence
  • fractional part
  • divisor
  • prime divisor
  • uniform distribution

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