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

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## 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 *q ^{k}* and

*n*, where

^{2}*q*

^{k}*n*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

^{2}*q*.

### Keywords

- Odd perfect number
- Abundancy index
- Euler prime

### AMS Classification

- 11A25

### References

- 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.
- Dris, J. A. B. (2012) The abundancy index of divisors of odd perfect numbers, J. Integer Seq., 15, Article 12.4.4.

## Related papers

- Dris, J. A. B. (2020). On the quantity
*I*(*q*) +^{k}*I*(*n*^{2}) where*q*is an odd perfect number. Notes on Number Theory and Discrete Mathematics, 26 (3), 25-32, doi: 10.7546/nntdm.2020.26.3.25-32.^{k}n^{2}

## Cite this paper

APADris, 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.

ChicagoDris, 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.

MLADris, 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.