Prime divisors in Beatty sequences Original Research Article

We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence left floorαn+βright floor, image, where image, and α>0 is irrational. For example, we show thatimage where Ω(k) and ω(k) denote the number of prime divisors of an integer k≠0 counted with and without multiplicities, respectively.