On consecutive integers divisible by the number of their divisors

• Autorzy: Titu Andreescu , Florian Luca , M. Tip Phaovibul
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11N25: Distribution of integers with specified multiplicative constraints
• 11N64: Other results on the distribution of values or the characterization of arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 3
• Strony: 269-281

Daty

wydano

2016

Twórcy

autor

Titu Andreescu

• Department of Science/Mathematics Education, The University of Texas at Dallas, FN32, 800 West Campbell Road, Richardson, TX 75080-3021, U.S.A.

autor

Florian Luca

• School of Mathematics, University of the Witwatersrand, Private Bag X3, Wits 2050, Johannesburg, South Africa

autor

M. Tip Phaovibul

• P.O. Box 749, Mosier, OR 97040, U.S.A.

Identyfikatory

DOI

10.4064/aa8242-1-2016