Abstract
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 $10^{14}$.
Citation
Takeshi Goto. Katsuyuki Okeya. "All Harmonic Numbers Less than $10^{14}$." Japan J. Indust. Appl. Math. 24 (3) 275 - 288, October 2007.
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