Prime divisors in Beatty sequences
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William D. Banks; Igor E. Shparlinski
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Article
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2007
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Elsevier Science
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English
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We study the values of arithmetic functions taken on the elements of a non-homogeneous Beatty sequence ฮฑn + ฮฒ , n = 1, 2, . . . , where ฮฑ, ฮฒ โ R, and ฮฑ > 0 is irrational. For example, we show that where ฮฉ(k) and ฯ(k) denote the number of prime divisors of an integer k = 0 counted with and without m