A note on the OEIS sequence A228059

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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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 p1+4kr2, where p is prime of the form 1+4m, 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

  1. Adajar, C. F. E., OEIS sequence A271816 – Deficient-perfect numbers: Deficient numbers n such that n/(2n – (n)) is an integer, http://oeis.org/A271816.
  2. Beasley, B. D. (2013). Euler and the ongoing search for odd perfect numbers, ACMS 19th Biennial Conference Proceedings, Bethel University.
  3. Dickson, L. E. (1971). History of the theory of numbers, Vol. 1, pp. 3-33 (Chelsea Pub. Co., New York).
  4. 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.
  5. Holdener, J. A. (2006). Conditions equivalent to the existence of odd perfect numbers, Math. Mag., 79, 389-391.
  6. Noe, T. D., OEIS sequence A228059, http://oeis.org/A228059.
  7. Resta, G., Private communication, August 23, 2018.
  8. Resta, G., Private communication, August 24, 2018.
  9. Sloane, N. J. A., OEIS sequence A033879 – Deficiency of n, or 2nσ(n), http://oeis. org/A033879.
  10. Sorli, R. M. (2003). Algorithms in the study of multiperfect and odd perfect numbers, Ph. D. Thesis, University of Technology, Sydney.

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Cite this paper

APA

Dris, 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.

Chicago

Dris, 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.

MLA

Dris, 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.

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