On locally repeated values of certain arithmetic functions. III

Erdős, Paul; Pomerance, Carl; Sárközy, András

doi:10.1090/S0002-9939-1987-0897061-6

On locally repeated values of certain arithmetic functions. III
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by Paul Erdős, Carl Pomerance and András Sárközy PDF

Proc. Amer. Math. Soc. 101 (1987), 1-7 Request permission

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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