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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 781.11011

**Autor: ** Erdös, Paul; Zhang, Zhenxiang

**Title: ** Upper bound of **sum** 1/(a_{i} log a_{i}) for quasi-primitive sequences. (In English)

**Source: ** Comput. Math. Appl. 26, No.3, 1-5 (1993).

**Review: ** A strictly increasing sequence A = **{**a_{i}**}** is said to be primitive if no element of A divides any other. Similarly, A is called quasi- primitive if the equation (a_{i},a_{j}) = a_{r} 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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag