Jose Arnaldo Bebita Dris and Doli-Jane Uvales Tejada

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 25, 2019, Number 1, Pages 199—205

DOI: 10.7546/nntdm.2019.25.1.199-205

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## Details

### Authors and affiliations

Jose Arnaldo Bebita Dris

*Institute of Mathematics, University of the Philippines
Carlos P. Garcia Avenue, Diliman, Quezon City, Philippines
*

Doli-Jane Uvales Tejada

*Mathematics Department, College of Natural Sciences and Mathematics
Mindanao State University, General Santos City, Philippines
*

### Abstract

The OEIS sequence A228059 lists odd numbers of the form *p*^{1+4k}*r*^{2}, where *p* is prime of the form 1+4*m*, *r* > 1, and gcd(*p, r*) = 1 that are closer to being perfect than previous terms. In this note, we present the prime factorizations of the first 37 terms.

### Keywords

- Odd perfect number
- Abundancy index
- Deficiency

### 2010 Mathematics Subject Classification

- 11A25

### References

- Adajar, C. F. E., OEIS sequence A271816 – Deficient-perfect numbers: Deficient numbers
*n*such that*n*/(2*n*– (*n*)) is an integer, http://oeis.org/A271816. - Beasley, B. D. (2013). Euler and the ongoing search for odd perfect numbers, ACMS 19th Biennial Conference Proceedings, Bethel University.
- Dickson, L. E. (1971). History of the theory of numbers, Vol. 1, pp. 3-33 (Chelsea Pub. Co., New York).
- Dris, J. A. B. (2017). Conditions equivalent to the Descartes–Frenicle–Sorli conjecture on odd perfect numbers, Notes on Number Theory and Discrete Mathematics, 23 (2), 12-20.
- Holdener, J. A. (2006). Conditions equivalent to the existence of odd perfect numbers, Math. Mag., 79, 389-391.
- Noe, T. D., OEIS sequence A228059, http://oeis.org/A228059.
- Resta, G., Private communication, August 23, 2018.
- Resta, G., Private communication, August 24, 2018.
- Sloane, N. J. A., OEIS sequence A033879 – Deficiency of
*n*, or 2*n*–*σ*(*n*), http://oeis. org/A033879. - Sorli, R. M. (2003). Algorithms in the study of multiperfect and odd perfect numbers, Ph. D. Thesis, University of Technology, Sydney.

## Related papers

## Cite this paper

APADris, J. A. B. & Tejada, D.-J. U. (2019). A note on the OEIS sequence A228059. Notes on Number Theory and Discrete Mathematics, 25(1), 199-205, doi: 10.7546/nntdm.2019.25.1.199-205.

ChicagoDris, Jose Arnaldo Bebita and Doli-Jane Uvales Tejada. “A Note on the OEIS Sequence A228059.” Notes on Number Theory and Discrete Mathematics 25, no. 1 (2019): 199-205, doi: 10.7546/nntdm.2019.25.1.199-205.

MLADris, Jose Arnaldo Bebita and Doli-Jane Uvales Tejada. “A Note on the OEIS Sequence A228059.” Notes on Number Theory and Discrete Mathematics 25.1 (2019): 199-205. Print, doi: 10.7546/nntdm.2019.25.1.199-205.