The first few weird numbers are 70, 836, 4030, 5830, 7192, 7912, 9272, (listed in A006037 of Sloane’s OEIS). All the known weird numbers are even. In 1972, Benkoski wondered if there are any odd weird numbers; to this day is an accepted lower bound. Despite this question of parity, it has been proven that there are infinitely many weird numbers and that they have positive Schnirelmann density.
Even so, weird numbers are rarer than semiperfect numbers; twice a weird number is usually a semiperfect number, which makes all subsequent multiples of a weird number also semiperfect.
The band Boards of Canada records for the label Music70. Track 9 of their album Geogaddi is titled ”The Smallest Weird Number.”
- 1 S. Benkoski, ”Are All Weird Numbers Even?”, Amer. Math. Monthly 79 (1972), 774.
- 2 Wikipedia, http://en.wikipedia.org/wiki/Weird_numberWeird number
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