Harmonic Divisor Number - Bounds and Computer Searches

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W. H. Mills (unpublished; see Muskat) showed that any odd harmonic divisor number above 1 must have a prime power factor greater than 107, and Cohen showed that any such number must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

Famous quotes containing the words bounds, computer and/or searches:

    What comes over a man, is it soul or mind
    That to no limits and bounds he can stay confined?
    You would say his ambition was to extend the reach
    Clear to the Arctic of every living kind.
    Why is his nature forever so hard to teach
    That though there is no fixed line between wrong and right,
    There are roughly zones whose laws must be obeyed?
    Robert Frost (1874–1963)

    Family life is not a computer program that runs on its own; it needs continual input from everyone.
    Neil Kurshan (20th century)

    When a person doesn’t understand something, he feels internal discord: however he doesn’t search for that discord in himself, as he should, but searches outside of himself. Thence a war develops with that which he doesn’t understand.
    Anton Pavlovich Chekhov (1860–1904)