完全数 (Japanese Wikipedia)

Analysis of information sources in references of the Wikipedia article "完全数" in Japanese language version.

refsWebsite

Global rank Japanese rank

8wolfram.com

513^th place

882^nd place

6doi.org

2^nd place

6^th place

5worldcat.org

5^th place

19^th place

4ams.org

451^st place

1,252^nd place

2lirmm.fr

low place

2byu.edu

1,687^th place

6,772^nd place

1archive.org

6^th place

146^th place

1web.archive.org

1^st place

1mersenne.org

low place

1colgate.edu

low place

1zbmath.org

1,923^rd place

3,500^th place

1arxiv.org

69^th place

227^th place

1uwaterloo.ca

3,153^rd place

5,934^th place

1tus.ac.jp

low place

2,380^th place

ams.org

mathscinet.ams.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. MR2904601.
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. MR2904606. 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. MR3356038.
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. MR2336286.

archive.org

Nicomachus of Gerasa (1926). Introduction to Arithmetic. Martin Luther D'Oge (trans). The Macmillan Company. pp. 207–212

arxiv.org

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. MR2336286.

byu.edu

math.byu.edu

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. MR3356038.
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. MR2336286.

colgate.edu

math.colgate.edu

Nielsen, Pace P. (2003). “An upper bound for odd perfect numbers”. Integers 3: A14.

doi.org

Grün, Otto (1952). “Über ungerade vollkommene Zahlen”. Mathematische Zeitschrift 55 (3): 353--354. doi:10.1007/BF01181133.
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. MR2904601.
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. MR2904606. 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. MR3356038.
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. MR2336286.

lirmm.fr

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. MR2904601.
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. MR2904606. Zbl 1263.11005.

mersenne.org

"GIMPS Discovers Largest Known Prime Number: 2^136,279,841-1" (Press release) (英語). GIMPS. 21 October 2024. 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

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

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

"GIMPS Discovers Largest Known Prime Number: 2^136,279,841-1" (Press release) (英語). GIMPS. 21 October 2024. 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。

wolfram.com

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. "Multiplicative Perfect Number". mathworld.wolfram.com (英語).

worldcat.org

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. MR2904601.
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. MR2904606. 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. MR3356038.
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. MR2336286.

zbmath.org

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. MR2904606. Zbl 1263.11005.