
doi: 10.1007/bf03167540
``A positive integer \(n\) is said to be \textit{harmonic} if the harmonic mean of its positive divisors \[ H(n)=\frac{n\tau(n)}{\sigma(n)} \] is an integer, where \(\tau(n)\) denotes the number of the positive divisors of \(n\).'' Properties of harmonic numbers, including their relationship to perfect numbers, have been studied by \textit{Ø. Ore} [Am. Math. Mon. 55, 615--619 (1948; Zbl 0031.10903)]. In this paper, the authors provide the list of all harmonic numbers less than \(10^{14}\). Answering a question of \textit{G. L. Cohen} and \textit{R. M. Sorli} [Fibonacci Q. 36, No. 5, 386--390 (1998; Zbl 0948.11004)], the authors show that every harmonic number does not have a unique harmonic seed.
Ore's conjecture, harmonic seed, harmonic number, Arithmetic functions; related numbers; inversion formulas, harmonic mean, perfect number, Values of arithmetic functions; tables
Ore's conjecture, harmonic seed, harmonic number, Arithmetic functions; related numbers; inversion formulas, harmonic mean, perfect number, Values of arithmetic functions; tables
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