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**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 **sum**_{pia_{i}||n}a_· p_{i}. 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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