Prime divisors in Beatty sequences

✍ Scribed by William D. Banks; Igor E. Shparlinski

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 137 KB
• Volume: 123
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.07.011

✦ Synopsis

We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence αn + β , n = 1, 2, . . . , where α, β ∈ R, and α > 0 is irrational. For example, we show that

where Ω(k) and ω(k) denote the number of prime divisors of an integer k = 0 counted with and without multiplicities, respectively.