On consecutive integers divisible by the number of their divisors

Titu Andreescu, Florian Luca, and M. Tip Phaovibul. "On consecutive integers divisible by the number of their divisors." Acta Arithmetica 173.3 (2016): 269-281. <http://eudml.org/doc/286183>.

@article{TituAndreescu2016,
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 ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.},
author = {Titu Andreescu, Florian Luca, M. Tip Phaovibul},
journal = {Acta Arithmetica},
keywords = {divisors; pell equations; sieve methods},
language = {eng},
number = {3},
pages = {269-281},
title = {On consecutive integers divisible by the number of their divisors},
url = {http://eudml.org/doc/286183},
volume = {173},
year = {2016},
}

TY - JOUR
AU - Titu Andreescu
AU - Florian Luca
AU - M. Tip Phaovibul
TI - On consecutive integers divisible by the number of their divisors
JO - Acta Arithmetica
PY - 2016
VL - 173
IS - 3
SP - 269
EP - 281
AB - 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.
LA - eng
KW - divisors; pell equations; sieve methods
UR - http://eudml.org/doc/286183
ER -