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Harmonic divisor number
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== Bounds and computer searches == W. H. Mills (unpublished; see Muskat) showed that any odd harmonic divisor number above 1 must have a prime power factor greater than 10<sup>7</sup>, and Cohen showed that any such number must have at least three different [[prime number|prime]] factors. {{harvtxt|Cohen|Sorli|2010}} showed that there are no odd harmonic divisor numbers smaller than 10<sup>24</sup>. Cohen, Goto, and others starting with Ore himself have performed computer searches listing all small harmonic divisor numbers. From these results, lists are known of all harmonic divisor numbers up to 2 Γ 10<sup>9</sup>, and all harmonic divisor numbers for which the harmonic mean of the divisors is at most 300.
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