All Harmonic Numbers Less than $10^{14}$
Goto, Takeshi ; Okeya, Katsuyuki
Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, p. 275-288 / Harvested from Project Euclid
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A positive integer $n$ is said to be \textit{harmonic} if the harmonic mean $H(n)$ of its positive divisors is an integer. Ore proved that every perfect number is harmonic and conjectured that there exist no odd harmonic numbers greater than $1$. In this article, we give the list of all harmonic numbers up to $10^{14}$. In particular, we find that there exist no nontrivial odd harmonic numbers less than $10^{14}$.
Publié le : 2007-10-14
Classification:  harmonic number,  perfect number,  Ore's conjecture 
@article{1197909113,
     author = {Goto, Takeshi and Okeya, Katsuyuki},
     title = {All Harmonic Numbers Less than $10^{14}$},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {24},
     number = {1},
     year = {2007},
     pages = { 275-288},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1197909113}
}

Goto, Takeshi; Okeya, Katsuyuki. All Harmonic Numbers Less than $10^{14}$. Japan J. Indust. Appl. Math., Tome 24 (2007) no. 1, pp.  275-288. http://gdmltest.u-ga.fr/item/1197909113/