Geodesic
On consecutive integers divisible by the number of their 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.
Acta Arithmetica, Tome 173 (2016) no. 3, pp. 269-281 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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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