On consecutive integers divisible by the number of their divisors
Volume 173 / 2016
Acta Arithmetica 173 (2016), 269-281
MSC: Primary 11N25; Secondary 11N41, 11N64.
DOI: 10.4064/aa8242-1-2016
Published online: 14 April 2016
Abstract
We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers $n\le x$ such that each of $n$ and $n+1$ is a multiple of the number of its divisors.
