Publications of (and about) Paul Erdös
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 a0(1) = n and define ai+1(n) > ai(n) inductively as the least integer coprime to aj(n) for 0 \leq j \leq i. Let g(n) be the largest ai(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 ai(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.
Classif.: * 11N05 Distribution of primes
11B83 Special sequences of integers and polynomials
Keywords: order of magnitude; distribution of integers; relatively prime sequences
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