A note on values of beatty sequences that are free of large prime factors

Akbal Y.

Colloquium Mathematicum, vol.160, no.1, pp.53-63, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 160 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.4064/cm7715-2-2019
  • Journal Name: Colloquium Mathematicum
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.53-63
  • Keywords: Beatty sequences, Exponential sums, Friable numbers
  • TED University Affiliated: No


Let α and β be fixed real numbers and suppose that α > 1 is irrational and of finite type. We study values of the non-homogeneous Beatty sequence (Formula Presented) that are free of large prime factors, where (Formula Presented) is the largest integer not exceeding x.