The divisor function at consecutive integers

Adolf J. Hildebrand

Vol. 129 (1987), No. 2, 307–319

DOI: 10.2140/pjm.1987.129.307

Abstract

Let d(n) be the divisor function. Improving a result of Heath-Brown, we show that for sufficiently large x, d(n) = d(n + 1) holds for ≫ x(log log x)⁻³ integers n ≤ x.

Mathematical Subject Classification 2000

Primary: 11N37

Milestones

Received: 18 March 1986

Revised: 10 October 1986

Published: 1 October 1987