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highly composite number
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(Definition)
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We call  a highly composite number if  for all  , where  is the number of divisors of  . The first several are 1, 2, 4, 6, 12, 24. The sequence is A002182 in Sloane's OEIS.
The integer  is superior highly composite if there is an  such that for all  ,
The first several superior highly composite numbers are 2, 6, 12, 60, 120, 360. The sequence is A002201 in Sloane's encyclopedia.
- 1
- L. Alaoglu and P. Erdös, On highly composite and similar numbers. Trans. Amer. Math. Soc. 56 (1944), 448-469. Available at www.jstor.org
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"highly composite number" is owned by Kevin OBryant.
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(view preamble)
| Also defines: |
superior highly composite number |
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Cross-references: composite, integer, OEIS, sequence, divisors, number
There are 3 references to this entry.
This is version 4 of highly composite number, born on 2003-06-11, modified 2006-12-08.
Object id is 4347, canonical name is HighlyCompositeNumber.
Accessed 7212 times total.
Classification:
| AMS MSC: | 11N56 (Number theory :: Multiplicative number theory :: Rate of growth of arithmetic functions) |
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Pending Errata and Addenda
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