Article A Criterion for Deficient Numbers Using the Abundancy Index and Deficiency Functions
Journal for Algebra and Number Theory Academia 8 (1), 1-9, 2018
Almost perfect number
Abundancy index
Deficiency
Posted by: Jose Arnaldo Bebita Dris
arXiv fulltext MSC 2010: 11A25
Article The Non-Euler Part Of A Spoof Odd Perfect Number Is Not Almost Perfect
Indian Journal in Number Theory, 6-12, 2018
Abundancy index
Spoof odd perfect number
Descartes number
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A05 11A25
Article Conditions equivalent to the Descartes–Frenicle–Sorli Conjecture on odd perfect numbers – Part II
Notes on Number Theory and Discrete Mathematics 24 (3), 62-67, 2018
Odd perfect number
Abundancy index
Deficiency
Posted by: Jose Arnaldo Bebita Dris
DOI fulltext MSC 2010: 11A25
Overview
The Descartes–Frenicle–Sorli conjecture predicts that $k=1$ if $q^k n^2$ is an odd perfect number with Euler prime $q$. In this note, we present some further conditions equivalent to this conjecture.
Article Revisiting some old results on odd perfect numbers
Notes on Number Theory and Discrete Mathematics 24 (4), 18-25, 2018
Odd perfect number
Descartes-Frenicle-Sorli conjecture
Dris conjecture
Abundancy index
Deficiency
Posted by: Jose Arnaldo Bebita Dris
DOI fulltext MSC 2010: 11A25
Overview
In this note, we revisit and show how some old results on odd perfect numbers follow from assuming some unproven yet reasonable conjectures.
Article Conditions equivalent to the Descartes-Frenicle-Sorli Conjecture on odd perfect numbers
Notes on Number Theory and Discrete Mathematics 23 (2), 12-20, 2017
Odd perfect number
Abundancy index
Deficiency
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A25
Article The Abundancy index of divisors of odd perfect numbers – Part III
Notes on Number Theory and Discrete Mathematics 23 (3), 53-59, 2017
Odd perfect number
Abundancy index
Euler prime
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A25
Article The Abundancy Index of Divisors of Spoof Odd Perfect Numbers
Indian Journal in Number Theory, 13-26, 2017
Abundancy index
Spoof odd perfect number
Descartes number
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A05 11A25
Article On a curious biconditional involving the divisors of odd perfect numbers
Notes on Number Theory and Discrete Mathematics 23 (4), 1-13, 2017
Odd perfect number
Abundancy index
Deficiency
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A25
Article New Results for the Descartes-Frenicle-Sorli Conjecture on Odd Perfect Numbers
Journal for Algebra and Number Theory Academia 6 (3), 95-114, 2016
Odd perfect number
Sorli's conjecture
Euler prime
Posted by: Jose Arnaldo Bebita Dris
fulltext MSC 2010: 11A05 11J25 11J99
Article A note on odd perfect numbers
Fibonacci Quarterly 54 (4), 291-295, 2016
Posted by: Jose Arnaldo Bebita Dris
arXiv fulltext MSC 2010: 11A25
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