완전수 (Korean Wikipedia)

Analysis of information sources in references of the Wikipedia article "완전수" in Korean language version.

refsWebsite

Global rank Korean rank

15doi.org

2^nd place

3^rd place

7worldcat.org

5^th place

11^th place

7ams.org

451^st place

121^st place

6semanticscholar.org

11^th place

310^th place

4harvard.edu

18^th place

27^th place

4arxiv.org

69^th place

54^th place

3colgate.edu

low place

2byu.edu

1,687^th place

1,020^th place

2math.ca

low place

1lirmm.fr

low place

1zbmath.org

1,923^rd place

99^th place

1austms.org.au

low place

1tus.ac.jp

low place

1westga.edu

low place

1albany.edu

7,412^th place

low place

1wikipedia.org

low place

albany.edu

nyjm.albany.edu

Pomerance, Carl; Luca, Florian (2010). “On the radical of a perfect number”. 《New York Journal of Mathematics》 16: 23–30. 2018년 12월 7일에 확인함.

ams.org

Iannucci, DE (1999). “The second largest prime divisor of an odd perfect number exceeds ten thousand” (PDF). 《Mathematics of Computation》 68 (228): 1749–1760. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6. 2011년 3월 30일에 확인함.
Iannucci, DE (2000). “The third largest prime divisor of an odd perfect number exceeds one hundred” (PDF). 《Mathematics of Computation》 69 (230): 867–879. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. 2011년 3월 30일에 확인함.
McDaniel, Wayne L. (1970). “The non-existence of odd perfect numbers of a certain form”. 《Archiv der Mathematik》 21 (1): 52–53. doi:10.1007/BF01220877. ISSN 1420-8938. MR 0258723. S2CID 121251041.
Kanold, Hans-Joachim (1950). “Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II”. 《Journal für die reine und angewandte Mathematik》 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579. S2CID 122452828.
Cohen, G. L.; Williams, R. J. (1985). “Extensions of some results concerning odd perfect numbers” (PDF). 《Fibonacci Quarterly》 23 (1): 70–76. ISSN 0015-0517. MR 0786364.
Hagis, Peter Jr.; McDaniel, Wayne L. (1972). “A new result concerning the structure of odd perfect numbers”. 《Proceedings of the American Mathematical Society》 32 (1): 13–15. doi:10.1090/S0002-9939-1972-0292740-5. ISSN 1088-6826. MR 0292740.
McDaniel, Wayne L.; Hagis, Peter Jr. (1975). “Some results concerning the non-existence of odd perfect numbers of the form $p^{\alpha }M^{2\beta }$ ” (PDF). 《Fibonacci Quarterly》 13 (1): 25–28. ISSN 0015-0517. MR 0354538. |title=에 지움 문자가 있음(위치 78) (도움말)

arxiv.org

Zelinsky, Joshua (July 2019). “Upper bounds on the second largest prime factor of an odd perfect number”. 《International Journal of Number Theory》 15 (6): 1183–1189. arXiv:1810.11734. doi:10.1142/S1793042119500659. S2CID 62885986. .
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors” (PDF). 《Mathematics of Computation》 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. S2CID 2767519. 2011년 3월 30일에 확인함.
Graeme Clayton, Cody Hansen (2023). “On inequalities involving counts of the prime factors of an odd perfect number” (PDF). 《Integers》 23. arXiv:2303.11974. 2023년 11월 29일에 확인함.
Yamada, Tomohiro (2019). “A new upper bound for odd perfect numbers of a special form”. 《Colloquium Mathematicum》 156 (1): 15–21. arXiv:1706.09341. doi:10.4064/cm7339-3-2018. ISSN 1730-6302. S2CID 119175632.

austms.org.au

Roberts, T (2008). “On the Form of an Odd Perfect Number” (PDF). 《Australian Mathematical Gazette》 35 (4): 244.

byu.edu

math.byu.edu

Nielsen, Pace P. (2015). “Odd perfect numbers, Diophantine equations, and upper bounds” (PDF). 《Mathematics of Computation》 84 (295): 2549–2567. doi:10.1090/S0025-5718-2015-02941-X. 2015년 8월 13일에 확인함.
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors” (PDF). 《Mathematics of Computation》 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. S2CID 2767519. 2011년 3월 30일에 확인함.

colgate.edu

math.colgate.edu

Bibby, Sean; Vyncke, Pieter; Zelinsky, Joshua (2021년 11월 23일). “On the Third Largest Prime Divisor of an Odd Perfect Number” (PDF). 《Integers》 21. 2021년 12월 6일에 확인함.
Zelinsky, Joshua (2021년 8월 3일). “On the Total Number of Prime Factors of an Odd Perfect Number” (PDF). 《Integers》 21. 2021년 8월 7일에 확인함.
Graeme Clayton, Cody Hansen (2023). “On inequalities involving counts of the prime factors of an odd perfect number” (PDF). 《Integers》 23. arXiv:2303.11974. 2023년 11월 29일에 확인함.

doi.org

dx.doi.org

Ochem, Pascal; Rao, Michaël (2012). “Odd perfect numbers are greater than 10¹⁵⁰⁰” (PDF). 《Mathematics of Computation》 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718. Zbl 1263.11005.
Kühnel, Ullrich (1950). “Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen”. 《Mathematische Zeitschrift》 (독일어) 52: 202–211. doi:10.1007/BF02230691. S2CID 120754476.
Goto, T; Ohno, Y (2008). “Odd perfect numbers have a prime factor exceeding 10⁸” (PDF). 《Mathematics of Computation》 77 (263): 1859–1868. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9. 2011년 3월 30일에 확인함.
Konyagin, Sergei; Acquaah, Peter (2012). “On Prime Factors of Odd Perfect Numbers”. 《International Journal of Number Theory》 8 (6): 1537–1540. doi:10.1142/S1793042112500935.
Iannucci, DE (1999). “The second largest prime divisor of an odd perfect number exceeds ten thousand” (PDF). 《Mathematics of Computation》 68 (228): 1749–1760. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6. 2011년 3월 30일에 확인함.
Zelinsky, Joshua (July 2019). “Upper bounds on the second largest prime factor of an odd perfect number”. 《International Journal of Number Theory》 15 (6): 1183–1189. arXiv:1810.11734. doi:10.1142/S1793042119500659. S2CID 62885986. .
Iannucci, DE (2000). “The third largest prime divisor of an odd perfect number exceeds one hundred” (PDF). 《Mathematics of Computation》 69 (230): 867–879. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. 2011년 3월 30일에 확인함.
Nielsen, Pace P. (2015). “Odd perfect numbers, Diophantine equations, and upper bounds” (PDF). 《Mathematics of Computation》 84 (295): 2549–2567. doi:10.1090/S0025-5718-2015-02941-X. 2015년 8월 13일에 확인함.
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors” (PDF). 《Mathematics of Computation》 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. S2CID 2767519. 2011년 3월 30일에 확인함.
Chen, Yong-Gao; Tang, Cui-E (2014). “Improved upper bounds for odd multiperfect numbers.”. 《Bulletin of the Australian Mathematical Society》 89 (3): 353–359. doi:10.1017/S0004972713000488.
Ochem, Pascal; Rao, Michaël (2014). “On the number of prime factors of an odd perfect number.”. 《Mathematics of Computation》 83 (289): 2435–2439. doi:10.1090/S0025-5718-2013-02776-7.
McDaniel, Wayne L. (1970). “The non-existence of odd perfect numbers of a certain form”. 《Archiv der Mathematik》 21 (1): 52–53. doi:10.1007/BF01220877. ISSN 1420-8938. MR 0258723. S2CID 121251041.
Kanold, Hans-Joachim (1950). “Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II”. 《Journal für die reine und angewandte Mathematik》 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579. S2CID 122452828.
Hagis, Peter Jr.; McDaniel, Wayne L. (1972). “A new result concerning the structure of odd perfect numbers”. 《Proceedings of the American Mathematical Society》 32 (1): 13–15. doi:10.1090/S0002-9939-1972-0292740-5. ISSN 1088-6826. MR 0292740.
Yamada, Tomohiro (2019). “A new upper bound for odd perfect numbers of a special form”. 《Colloquium Mathematicum》 156 (1): 15–21. arXiv:1706.09341. doi:10.4064/cm7339-3-2018. ISSN 1730-6302. S2CID 119175632.

harvard.edu

adsabs.harvard.edu

Goto, T; Ohno, Y (2008). “Odd perfect numbers have a prime factor exceeding 10⁸” (PDF). 《Mathematics of Computation》 77 (263): 1859–1868. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9. 2011년 3월 30일에 확인함.
Iannucci, DE (1999). “The second largest prime divisor of an odd perfect number exceeds ten thousand” (PDF). 《Mathematics of Computation》 68 (228): 1749–1760. Bibcode:1999MaCom..68.1749I. doi:10.1090/S0025-5718-99-01126-6. 2011년 3월 30일에 확인함.
Iannucci, DE (2000). “The third largest prime divisor of an odd perfect number exceeds one hundred” (PDF). 《Mathematics of Computation》 69 (230): 867–879. Bibcode:2000MaCom..69..867I. doi:10.1090/S0025-5718-99-01127-8. 2011년 3월 30일에 확인함.
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors” (PDF). 《Mathematics of Computation》 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. S2CID 2767519. 2011년 3월 30일에 확인함.

lirmm.fr

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

math.ca

fq.math.ca

Cohen, G. L.; Williams, R. J. (1985). “Extensions of some results concerning odd perfect numbers” (PDF). 《Fibonacci Quarterly》 23 (1): 70–76. ISSN 0015-0517. MR 0786364.
McDaniel, Wayne L.; Hagis, Peter Jr. (1975). “Some results concerning the non-existence of odd perfect numbers of the form $p^{\alpha }M^{2\beta }$ ” (PDF). 《Fibonacci Quarterly》 13 (1): 25–28. ISSN 0015-0517. MR 0354538. |title=에 지움 문자가 있음(위치 78) (도움말)

semanticscholar.org

api.semanticscholar.org

Kühnel, Ullrich (1950). “Verschärfung der notwendigen Bedingungen für die Existenz von ungeraden vollkommenen Zahlen”. 《Mathematische Zeitschrift》 (독일어) 52: 202–211. doi:10.1007/BF02230691. S2CID 120754476.
Zelinsky, Joshua (July 2019). “Upper bounds on the second largest prime factor of an odd perfect number”. 《International Journal of Number Theory》 15 (6): 1183–1189. arXiv:1810.11734. doi:10.1142/S1793042119500659. S2CID 62885986. .
Nielsen, Pace P. (2007). “Odd perfect numbers have at least nine distinct prime factors” (PDF). 《Mathematics of Computation》 76 (260): 2109–2126. arXiv:math/0602485. Bibcode:2007MaCom..76.2109N. doi:10.1090/S0025-5718-07-01990-4. S2CID 2767519. 2011년 3월 30일에 확인함.
McDaniel, Wayne L. (1970). “The non-existence of odd perfect numbers of a certain form”. 《Archiv der Mathematik》 21 (1): 52–53. doi:10.1007/BF01220877. ISSN 1420-8938. MR 0258723. S2CID 121251041.
Kanold, Hans-Joachim (1950). “Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II”. 《Journal für die reine und angewandte Mathematik》 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579. S2CID 122452828.
Yamada, Tomohiro (2019). “A new upper bound for odd perfect numbers of a special form”. 《Colloquium Mathematicum》 156 (1): 15–21. arXiv:1706.09341. doi:10.4064/cm7339-3-2018. ISSN 1730-6302. S2CID 119175632.

tus.ac.jp

ma.noda.tus.ac.jp

Goto, T; Ohno, Y (2008). “Odd perfect numbers have a prime factor exceeding 10⁸” (PDF). 《Mathematics of Computation》 77 (263): 1859–1868. Bibcode:2008MaCom..77.1859G. doi:10.1090/S0025-5718-08-02050-9. 2011년 3월 30일에 확인함.

westga.edu

Nielsen, Pace P. (2003). “An upper bound for odd perfect numbers”. 《Integers》 3: A14–A22. 2021년 3월 23일에 확인함.

wikipedia.org

de.wikipedia.org

Kanold, Hans-Joachim (1950). “Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II”. 《Journal für die reine und angewandte Mathematik》 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579. S2CID 122452828.

worldcat.org

Ochem, Pascal; Rao, Michaël (2012). “Odd perfect numbers are greater than 10¹⁵⁰⁰” (PDF). 《Mathematics of Computation》 81 (279): 1869–1877. doi:10.1090/S0025-5718-2012-02563-4. ISSN 0025-5718. Zbl 1263.11005.
McDaniel, Wayne L. (1970). “The non-existence of odd perfect numbers of a certain form”. 《Archiv der Mathematik》 21 (1): 52–53. doi:10.1007/BF01220877. ISSN 1420-8938. MR 0258723. S2CID 121251041.
Kanold, Hans-Joachim (1950). “Satze uber Kreisteilungspolynome und ihre Anwendungen auf einige zahlentheoretisehe Probleme. II”. 《Journal für die reine und angewandte Mathematik》 188 (1): 129–146. doi:10.1515/crll.1950.188.129. ISSN 1435-5345. MR 0044579. S2CID 122452828.
Cohen, G. L.; Williams, R. J. (1985). “Extensions of some results concerning odd perfect numbers” (PDF). 《Fibonacci Quarterly》 23 (1): 70–76. ISSN 0015-0517. MR 0786364.
Hagis, Peter Jr.; McDaniel, Wayne L. (1972). “A new result concerning the structure of odd perfect numbers”. 《Proceedings of the American Mathematical Society》 32 (1): 13–15. doi:10.1090/S0002-9939-1972-0292740-5. ISSN 1088-6826. MR 0292740.
McDaniel, Wayne L.; Hagis, Peter Jr. (1975). “Some results concerning the non-existence of odd perfect numbers of the form $p^{\alpha }M^{2\beta }$ ” (PDF). 《Fibonacci Quarterly》 13 (1): 25–28. ISSN 0015-0517. MR 0354538. |title=에 지움 문자가 있음(위치 78) (도움말)
Yamada, Tomohiro (2019). “A new upper bound for odd perfect numbers of a special form”. 《Colloquium Mathematicum》 156 (1): 15–21. arXiv:1706.09341. doi:10.4064/cm7339-3-2018. ISSN 1730-6302. S2CID 119175632.

zbmath.org

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