Prime divisors in Beatty sequences

نویسندگان

  • William D. Banks
  • Igor E. Shparlinski
  • Carl Pomerance
چکیده

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 ∑ n N ω ( αn+ β )∼N log logN and ∑ n N (−1)Ω( αn+β ) = o(N), where Ω(k) and ω(k) denote the number of prime divisors of an integer k = 0 counted with and without multiplicities, respectively. © 2006 Elsevier Inc. All rights reserved.

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تاریخ انتشار 2007