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**Zentralblatt MATH**

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

**Zbl.No: ** 399.10042

**Autor: ** Erdös, Paul; Penney, D.E.; Pomerance, Carl

**Title: ** On a class of relatively prime sequences. (In English)

**Source: ** J. Number Theory 10, 451-474 (1978).

**Review: ** For each n \geq 1 let a_{0}(1) = n and define a_{i+1}(n) > a_{i}(n) inductively as the least integer coprime to a_{j}(n) for 0 \leq j \leq i. Let g(n) be the largest a_{i}(n) which is neither a prime n or the square of a prime. It is shown here that g(n) ~ n and that g(n)-n >> m^{ ½} log n. The true order of magnitude of g(n)-n remains unsettled, and some relevant computations are discussed. Other results on the sequence a_{i}(n) are given, extending work of *P.Erdös* [Math. Mag. 51, 238-240 (1978; Zbl 391.10004)] . The following result occurs incidentally in one of the proofs: if n is large enough [n/p] is composite for some prime p < n^{ ½}.

**Reviewer: ** R.Heath-Brown

**Classif.: ** * 11N05 Distribution of primes

11B83 Special sequences of integers and polynomials

**Keywords: ** order of magnitude; distribution of integers; relatively prime sequences

**Citations: ** Zbl.391.10004

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