完全数 (Japanese Wikipedia)

Euler (1849)は. 1747年2月23日にベルリン・アカデミーにより査読され、オイラーの死後の1849年に出版された。特に 88頁の§8を参照^[7]。 Euler, Leonhard (1849), “De numeris amicibilibus [On amicable numbers]” (ラテン語), Commentationes arithmeticae, 2, pp. 627–636

mersenne.org (Global: low place; Japanese: low place)

“GIMPS Discovers Largest Known Prime Number: 2^136,279,841-1” (Press release) (英語). GIMPS. 2024年10月21日. 2024年11月19日時点のオリジナルよりアーカイブ. 2024年11月21日閲覧.

tus.ac.jp (Global: low place; Japanese: 2,160^th place)

ma.noda.tus.ac.jp

T. Goto and Y. Ohno, "Odd perfect numbers have a prime factor exceeding 10⁸", Math. Comp. 77 (2008), 1859-1868. "奇数の完全数の最大素因子について" - preprint を入手可能。

uwaterloo.ca (Global: 3,649^th place; Japanese: 5,866^th place)

math.uwaterloo.ca

75個以上であることを示した、以前の結果は K. G. Hare, "New techniques for bounds on the total number of prime factors of an odd perfect number", Math. Comp. 76. (2007), 2241-2248. preprint

web.archive.org (Global: 1^st place; Japanese: 1^st place)

“GIMPS Discovers Largest Known Prime Number: 2^136,279,841-1” (Press release) (英語). GIMPS. 2024年10月21日. 2024年11月19日時点のオリジナルよりアーカイブ. 2024年11月21日閲覧.
Pomerance's Heuristic that Odd Perfect Numbers are Unlikely

wolfram.com (Global: 1,091^st place; Japanese: 1,223^rd place)

mathworld.wolfram.com

Weisstein, Eric W. “Multiperfect Number”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Deficient Number”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Abundant Number”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Amicable Pair”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Sociable Numbers”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Quasiperfect Number”. mathworld.wolfram.com (英語).
Weisstein, Eric W. “Almost Perfect Number”. mathworld.wolfram.com (英語).
Weisstein, Eric W.. “Unitary Perfect Number” (英語). mathworld.wolfram.com. 2026年4月13日閲覧。
Weisstein, Eric W. “Multiplicative Perfect Number”. mathworld.wolfram.com (英語).

worldcat.org (Global: 4^th place; Japanese: 12^th place)

search.worldcat.org

Fletcher, S. Adam; Nielsen, Pace P.; Ochem, Pascal (2012). “Sieve methods for odd perfect numbers”. Mathematics of Computation 81 (279): 1753--1776. doi:10.1090/S0025-5718-2011-02576-7. ISSN 0025-5718. MR 2904601.
Yamada, Tomohiro (2019). “A new upper bound for odd perfect numbers of a special form”. Colloquium Mathematicum 156 (1): 15--21. doi:10.4064/cm7339-3-2018. ISSN 1730-6302.
Ochem, Pascal; Rao, Michaël (2012). “Odd perfect numbers are greater than 10¹⁵⁰⁰”. Mathematics of Computation 81 (279): 1869--1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718. MR 2904606. Zbl 1263.11005.
Nielsen, Pace P. (2015). “Odd perfect numbers, Diophantine equations, and upper bounds”. Mathematics of Computation 84 (295): 2549--2567. doi:10.1090/S0025-5718-2015-02941-X. ISSN 0025-5718. MR 3356038.
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors”. Mathematics of Computation 76 (260): 2109--2126. arXiv:math/0602485. doi:10.1090/S0025-5718-07-01990-4. ISSN 0025-5718. MR 2336286.

zbmath.org (Global: 2,089^th place; Japanese: 3,822^nd place)

Ochem, Pascal; Rao, Michaël (2012). “Odd perfect numbers are greater than 10¹⁵⁰⁰”. Mathematics of Computation 81 (279): 1869--1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718. MR 2904606. Zbl 1263.11005.

完全数 (Japanese Wikipedia)

ams.org (Global: 434th place; Japanese: 1,052nd place)

mathscinet.ams.org

archive.org (Global: 6th place; Japanese: 87th place)

arxiv.org (Global: 49th place; Japanese: 115th place)

byu.edu (Global: 1,502nd place; Japanese: 6,540th place)

math.byu.edu

colgate.edu (Global: low place; Japanese: low place)

math.colgate.edu

doi.org (Global: 2nd place; Japanese: 3rd place)

lirmm.fr (Global: low place; Japanese: low place)

maa.org (Global: 4,358th place; Japanese: 9,836th place)

eulerarchive.maa.org

mersenne.org (Global: low place; Japanese: low place)

tus.ac.jp (Global: low place; Japanese: 2,160th place)

ma.noda.tus.ac.jp

uwaterloo.ca (Global: 3,649th place; Japanese: 5,866th place)

math.uwaterloo.ca

web.archive.org (Global: 1st place; Japanese: 1st place)

wolfram.com (Global: 1,091st place; Japanese: 1,223rd place)

mathworld.wolfram.com

worldcat.org (Global: 4th place; Japanese: 12th place)

search.worldcat.org

zbmath.org (Global: 2,089th place; Japanese: 3,822nd place)

ams.org (Global: 434^th place; Japanese: 1,052^nd place)

archive.org (Global: 6^th place; Japanese: 87^th place)

arxiv.org (Global: 49^th place; Japanese: 115^th place)

byu.edu (Global: 1,502^nd place; Japanese: 6,540^th place)

doi.org (Global: 2^nd place; Japanese: 3^rd place)

maa.org (Global: 4,358^th place; Japanese: 9,836^th place)

tus.ac.jp (Global: low place; Japanese: 2,160^th place)

uwaterloo.ca (Global: 3,649^th place; Japanese: 5,866^th place)

web.archive.org (Global: 1^st place; Japanese: 1^st place)

wolfram.com (Global: 1,091^st place; Japanese: 1,223^rd place)

worldcat.org (Global: 4^th place; Japanese: 12^th place)

zbmath.org (Global: 2,089^th place; Japanese: 3,822^nd place)