The abundancy index of divisors of odd perfect numbers – Part III

Jose Arnaldo B. Dris
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 23, 2017, Number 3, Pages 53—59
Download full paper: PDF, 139 Kb

Details

Authors and affiliations

Jose Arnaldo B. Dris
Department of Mathematics and Physics, Far Eastern University
Nicanor Reyes Street, Sampaloc, Manila, Philippines

Abstract

Dris gave numerical bounds for the sum of the abundancy indices of qk and n2, where qkn2 is an odd perfect number, in his master’s thesis. In this note, we show that improving the limits for this sum is equivalent to obtaining nontrivial bounds for the Euler prime q.

Keywords

  • Odd perfect number
  • Abundancy index
  • Euler prime

AMS Classification

  • 11A25

References

  1. Dris, J. A. B. (2008) Solving the Odd Perfect Number Problem: Some Old and New Approaches, M. Sc. Math thesis, De La Salle University, Manila, Philippines.
  2. Dris, J. A. B. (2012) The abundancy index of divisors of odd perfect numbers, J. Integer Seq., 15, Article 12.4.4.

Related papers

Cite this paper

APA

Dris, J. A. B. (2017). The abundancy index of divisors of odd perfect numbers – Part III. Notes on Number Theory and Discrete Mathematics, 23(3), 53-59.

Chicago

Dris, Jose Arnaldo B. “The abundancy index of divisors of odd perfect numbers – Part III.” Notes on Number Theory and Discrete Mathematics 23, no. 3 (2017): 53-59.

MLA

Dris, Jose Arnaldo B. “The abundancy index of divisors of odd perfect numbers – Part III.” Notes on Number Theory and Discrete Mathematics 23.3 (2017): 53-59. Print.

Comments are closed.