| Weird Number |
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The first weird number is 70, because its proper divisors are 1, 2, 5, 7, 10, 14, and 35; which sum to 74, but no subset of these sums to 70. The number 12 is abundant but not a ''weird number'' because the proper divisors of 12 are 1, 2, 3, 4, and 6; which sum to 16, but 2+4+6 = 12. The first few weird numbers are 70 , 836, 4030, 5830, 7192, 7912, 9272, 10430, ... . It has been shown that an infinite number of weird numbers exist, and the sequence of weird numbers has also been proven to have positive Asymptotic Density . It is not known if any odd weird numbers exist; if any do, they must be greater than 1018 (as noted by Bob Hearn in a July 2005 posting to the SeqFans mailing list ). SEE ALSO EXTERNAL LINKS |
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