Some new results concerning the equation , 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 , 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.
Revised:
Accepted:
Published online:
Classification: 11A25, 11A05, 11D61, 11J86
Keywords: Odd perfect numbers, multiperfect numbers, superperfect number; the sum of divisors, arithmetic functions, exponential diophantine equations.
Author's affiliations:
@article{JTNB_2020__32_1_259_0, author = {Tomohiro Yamada}, title = {On finiteness of odd superperfect numbers}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {259--274}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {32}, number = {1}, year = {2020}, doi = {10.5802/jtnb.1121}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1121/} }
TY - JOUR TI - On finiteness of odd superperfect numbers JO - Journal de Théorie des Nombres de Bordeaux PY - 2020 DA - 2020/// SP - 259 EP - 274 VL - 32 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1121/ UR - https://doi.org/10.5802/jtnb.1121 DO - 10.5802/jtnb.1121 LA - en ID - JTNB_2020__32_1_259_0 ER -
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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