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Proceedings of the American Mathematical Society

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On locally repeated values of certain arithmetic functions. III


Authors: Paul Erdős, Carl Pomerance and András Sárközy
Journal: Proc. Amer. Math. Soc. 101 (1987), 1-7
MSC: Primary 11A25
MathSciNet review: 897061
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Abstract: Let $ d(n)$ denote the number of natural divisors of $ n$. It is shown that the number of $ n \leq x$ with $ d(n) = d(n + 1)$ is $ O(x/\sqrt {\log \log x} )$. In addition, certain related problems and results are presented.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0897061-6
Article copyright: © Copyright 1987 American Mathematical Society