Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  379.10027
Autor:  Erdös, Paul; Pomerance, Carl
Title:  On the largest prime factors of n and n+1. (In English)
Source:  Aequationes Math. 17, 311-321 (1978).
Review:  The authors prove some interesting results which give a comparison of the largest prime factors of n and n+1. Let P(n) denote the largest prime factor of n. Then one of the impressive results proved is that the number of n \leq x for which P(n) > P(n+1) is >> x for all large x. Another of them is about numbers n for which f(n) = f(n+1) where by f(n) we mean sumpia_{i||n}a_· pi. Such numbers are called Aaron numbers. The authors prove that the number of Aaron numbers \leq x is O\epsilon(x(log x)-1+\epsilon). The results can find other attractive results in the body of the paper.
Reviewer:  K.Ramachandra
Classif.:  * 11N05 Distribution of primes
                   11N37 Asymptotic results on arithmetic functions
                   11A41 Elemementary prime number theory

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