Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 781.11011
Autor: Erdös, Paul; Zhang, Zhenxiang
Title: Upper bound of sum 1/(ai log ai) for quasi-primitive sequences. (In English)
Source: Comput. Math. Appl. 26, No.3, 1-5 (1993).
Review: A strictly increasing sequence A = {ai} is said to be primitive if no element of A divides any other. Similarly, A is called quasi- primitive if the equation (ai,aj) = ar has no solutions with r < i < j. Erdös has conjectured that f(A) \leq f(P) < 1.64 for any primitive sequence A, where P is the primitive sequence of all primes. The authors had shown in a previous paper [Proc. Am. Math. Soc. 117, No. 4, 891-895 (1993; Zbl 776.11013)] that f(A) \leq 1.84 for any primitive sequence.
In this paper, they conjecture a corresponding bound for quasi-primitive namely that f(A) \leq f(Q) < 2· 01 for any quasi-primitive sequence A, where Q is the quasi-primitive sequence of all prime powers, and prove that f(A) \leq 2.77 for any quasi-primitive sequence A.
Reviewer: M.Nair (Glasgow)
Classif.: * 11B83 Special sequences of integers and polynomials
Keywords: upper bound; primitive sequence; quasi-primitive sequence
Citations: Zbl 776.11013
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