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W. H. Mills (unpublished; see Muskat) showed that any odd harmonic divisor number above 1 must have a prime power factor greater than 107, and Cohen showed that any such number must have at least three different prime factors. Cohen and Sorli (2010) showed that there are no odd harmonic divisor numbers smaller than 1024.
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 2×109, and all harmonic divisor numbers for which the harmonic mean of the divisors is at most 300.
Read more about this topic: Harmonic Divisor Number
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“At bounds of boundless void.”
—Samuel Beckett (1906–1989)
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
—Gerald M. Edelman (b. 1928)
“The thing about Proust is his combination of the utmost sensibility with the utmost tenacity. He searches out these butterfly shades to the last grain. He is as tough as catgut and as evanescent as a butterfly’s bloom.”
—Virginia Woolf (1882–1941)