Primitive Sequences and Sets of Multiples

H. Halberstam and K. F. Roth
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H. Halberstam: University of Illinois, Department of Mathematics
K. F. Roth: Imperial College of Science and Technology, Department of Mathematics

Chapter V in Sequences, 1983, pp 238-274 from Springer

Abstract: Abstract Throughout this chapter A = {a i } will denote a subsequence of the sequence of natural numbers. We consider the set ℬ = ℬ(A) consisting of all the distinct positive multiples of elements of A. We note that ℬ is the positive part of the union, taken over all elements a i of A, of the congruence classes 0 (mod a i ). Whilst none of our arguments will depend on ordering ℬ, it will often be convenient (to facilitate description and for reasons of notation) to imagine ℬ to be ordered according to magnitude and to refer to it as a ‘sequence’.

Keywords: Natural Number; Prime Factor; Infinite Sequence; Congruence Class; Asymptotic Density (search for similar items in EconPapers)
Date: 1983
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DOI: 10.1007/978-1-4613-8227-0_5

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