Odd Spoof Multiperfect Numbers of Higher Order
Grand Duchy of Luxembourg
L-8476 Eischen
E-mail: uk.laszlo.toth@gmail.com
Received:
Received: 21 March 2025; accepted: 5 August 2025; published online: 10 September 2025
DOI: 10.12921/cmst.2025.0000006
Abstract:
We extend our previous work on odd spoof multiperfect numbers to the case where spoof factor multiplicities exceed 2. This leads to the idenfitication of 11 new integers that would be odd multiperfect numbers if one of their prime factors had higher multiplicity. An example is 181 545, which would be an odd multiperfect number if only one of its prime factors, 3, had multiplicity 5.
Key words:
Descartes numbers, multiperfect numbers, odd perfect numbers
References:
[1] N. Andersen, S. Durham, M. Griffin, J. Hales, P. Jenkins, R. Keck, H. Ko, G. Molnar, E. Moss, P. Nielsen, K. Niendorf, V. Tombs, M. Warnick, D. Wu, Odd, spoof perfect factorizations, J. Number Theory 234, 31–47 (2022).
[2] G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63, 187–213 (1984).
[3] L. Tóth, On the Density of Spoof Odd Perfect Numbers, Comput. Methods Sci. Technol. 27(1), 25–28 (2021).
[4] L. Tóth, Odd Spoof Multiperfect Numbers, Integers 25, Art. A19 (2025).
We extend our previous work on odd spoof multiperfect numbers to the case where spoof factor multiplicities exceed 2. This leads to the idenfitication of 11 new integers that would be odd multiperfect numbers if one of their prime factors had higher multiplicity. An example is 181 545, which would be an odd multiperfect number if only one of its prime factors, 3, had multiplicity 5.
Key words:
Descartes numbers, multiperfect numbers, odd perfect numbers
References:
[1] N. Andersen, S. Durham, M. Griffin, J. Hales, P. Jenkins, R. Keck, H. Ko, G. Molnar, E. Moss, P. Nielsen, K. Niendorf, V. Tombs, M. Warnick, D. Wu, Odd, spoof perfect factorizations, J. Number Theory 234, 31–47 (2022).
[2] G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothèse de Riemann, J. Math. Pures Appl. 63, 187–213 (1984).
[3] L. Tóth, On the Density of Spoof Odd Perfect Numbers, Comput. Methods Sci. Technol. 27(1), 25–28 (2021).
[4] L. Tóth, Odd Spoof Multiperfect Numbers, Integers 25, Art. A19 (2025).
