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Harmonic divisor number
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== References == {{portal|Mathematics}} *{{cite web | author = Bogomolny, Alexander | title = An Identity Concerning Averages of Divisors of a Given Integer | url = http://www.cut-the-knot.org/proofs/average.shtml | access-date = 2006-09-10| author-link = Alexander Bogomolny }} *{{cite journal | last = Cohen | first = Graeme L. | url =https://www.ams.org/mcom/1997-66-218/S0025-5718-97-00819-3/S0025-5718-97-00819-3.pdf | title = Numbers Whose Positive Divisors Have Small Integral Harmonic Mean | journal = [[Mathematics of Computation]] | volume = 66 | pages = 883–891 | year = 1997 | doi = 10.1090/S0025-5718-97-00819-3 | issue = 218 | doi-access = free }} *{{cite journal | last1=Cohen | first1=Graeme L. | last2=Sorli | first2=Ronald M. | year=2010 | pages=2451 | title=Odd harmonic numbers exceed 10<sup>24</sup> | volume=79 | doi= 10.1090/S0025-5718-10-02337-9 | journal=Mathematics of Computation | issn=0025-5718 | issue=272 | doi-access=free | hdl=10453/13014 | hdl-access=free }} *{{cite web | author = Goto, Takeshi | url = http://www.ma.noda.tus.ac.jp/u/tg/harmonic-e.html | title = (Ore's) Harmonic Numbers | access-date = 2006-09-10 | archive-date = 2006-01-06 | archive-url = https://web.archive.org/web/20060106230537/http://www.ma.noda.tus.ac.jp/u/tg/harmonic-e.html | url-status = dead }} * {{cite book |last=Guy | first=Richard K. | author-link=Richard K. Guy | title=Unsolved problems in number theory | publisher=[[Springer-Verlag]] |edition=3rd | year=2004 |isbn=978-0-387-20860-2 | zbl=1058.11001 | at=B2 }} *{{cite journal | title = On Divisors of Odd Perfect Numbers | author = Muskat, Joseph B. | journal = Mathematics of Computation | volume = 20 | issue = 93 | year = 1966 | pages = 141–144 | doi = 10.2307/2004277 | jstor = 2004277| doi-access = free }} *{{cite journal | author = Ore, Øystein | author-link = Øystein Ore | title = On the averages of the divisors of a number | journal = [[American Mathematical Monthly]] | volume = 55 | year = 1948 | pages = 615–619 | doi = 10.2307/2305616 | issue = 10 | jstor = 2305616}} * {{MathWorld |title=Harmonic Divisor Number |urlname=HarmonicDivisorNumber}} {{Divisor classes}} {{Classes of natural numbers}} [[Category:Divisor function]] [[Category:Integer sequences]] [[Category:Number theory]] [[Category:Perfect numbers]]
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