On finiteness of odd superperfect numbers
Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 1, pp. 259-274.

Some new results concerning the equation σ(N)=aM, σ(M)=bN are proved. As a corollary, there are only finitely many odd superperfect numbers with a fixed number of distinct prime factors.

On montre de nouveaux résultats sur l’équation σ(N)=aM, σ(M)=bN. On en déduit, comme corollaire, qu’il n’existe qu’un nombre fini de nombres impairs superparfaits ayant un nombre fixé de facteurs premiers distincts.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1121
Classification: 11A25, 11A05, 11D61, 11J86
Keywords: Odd perfect numbers, multiperfect numbers, superperfect number; the sum of divisors, arithmetic functions, exponential diophantine equations.
Tomohiro Yamada 1

1 Center for Japanese language and culture, Osaka University, 562-8558, 8-1-1, Aomatanihigashi, Minoo, Osaka, Japan
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Tomohiro Yamada. On finiteness of odd superperfect numbers. Journal de théorie des nombres de Bordeaux, Volume 32 (2020) no. 1, pp. 259-274. doi : 10.5802/jtnb.1121. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1121/

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