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On Locally Repeated Values of Certain Arithmetic Functions. III

Paul Erdös, Carl Pomerance and András Sárközy
Proceedings of the American Mathematical Society
Vol. 101, No. 1 (Sep., 1987), pp. 1-7
DOI: 10.2307/2046541
Stable URL: http://www.jstor.org/stable/2046541
Page Count: 7
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On Locally Repeated Values of Certain Arithmetic Functions. III
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Abstract

Let d(n) denote the number of natural divisors of n. It is shown that the number of n ≤ 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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