Geodesic
On consecutive integers divisible by the number of their divisors
Titu Andreescu1 ; Florian Luca2 ; M. Tip Phaovibul3
1 Department of Science/Mathematics Education The University of Texas at Dallas FN32, 800 West Campbell Road Richardson, TX 75080-3021, U.S.A.
2 School of Mathematics University of the Witwatersrand Private Bag X3, Wits 2050 Johannesburg, South Africa
3 P.O. Box 749 Mosier, OR 97040, U.S.A.
Acta Arithmetica, Tome 173 (2016) no. 3, pp. 269-281

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/aa8242-1-2016
Keywords: prove there strings three consecutive integers each divisible number its divisors estimate number positive integers each multiple number its divisors

Titu Andreescu 1 ; Florian Luca 2 ; M. Tip Phaovibul 3

1 Department of Science/Mathematics Education The University of Texas at Dallas FN32, 800 West Campbell Road Richardson, TX 75080-3021, U.S.A.
2 School of Mathematics University of the Witwatersrand Private Bag X3, Wits 2050 Johannesburg, South Africa
3 P.O. Box 749 Mosier, OR 97040, U.S.A. 
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Titu Andreescu; Florian Luca; M. Tip Phaovibul. On consecutive integers divisible by the number of their divisors. Acta Arithmetica, Tome 173 (2016) no. 3, pp. 269-281. doi: 10.4064/aa8242-1-2016

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