On locally repeated values of certain arithmetic functions. III-Reference-Cited by-同舟云学术

On locally repeated values of certain arithmetic functions. III

Published:1987 Issue:1 Volume:101 Page:1-7
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Erdős Paul,Pomerance Carl,Sárközy András

Abstract

Let d ( n ) d(n) denote the number of natural divisors of n n . It is shown that the number of n ≤ x n \leq x with d ( n ) = d ( n + 1 ) d(n) = d(n + 1) is O ( x / log ⁡ log ⁡ x ) O(x/\sqrt {\log \log x} ) . In addition, certain related problems and results are presented.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1987-101-01/S0002-9939-1987-0897061-6/S0002-9939-1987-0897061-6.pdf

Reference8 articles.

1. P. T. Bateman and C. A. Spiro, private communication.

2. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences];Elliott, P. D. T. A.,1979

3. On locally repeated values of certain arithmetic functions. I;Erdős, P.;J. Number Theory,1985

4. On locally repeated values of certain arithmetic functions. II;Erdős, P.;Acta Math. Hungar.,1987

5. London Mathematical Society Monographs, No. 4;Halberstam, H.,1974

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