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 ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa8242-1-2016,
author = {Titu Andreescu and Florian Luca and M. Tip Phaovibul},
title = {On consecutive integers divisible by the number of their divisors},
journal = {Acta Arithmetica},
volume = {172},
year = {2016},
pages = {269-281},
zbl = {06602741},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8242-1-2016}
}
Titu Andreescu; Florian Luca; M. Tip Phaovibul. On consecutive integers divisible by the number of their divisors. Acta Arithmetica, Tome 172 (2016) pp. 269-281. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8242-1-2016/