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A060652
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Orders of non-Abelian groups.
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4
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6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 39, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 75, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 93, 94, 96, 98, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Because of the existence of a non-Abelian dihedral group of order 2n for each n>2 all the even numbers >= 6 are in this sequence.
What exactly are these numbers? - N. J. A. Sloane (njas(AT)research.att.com), Oct 09 2006
The non-Abelian orders (or non-Abelian numbers): n such that some group of order n is non-Abelian.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| Let the prime factorization of n be p1^e1...pr^e^r. Then n is in this sequence if ei>2 for some i or pi^k = 1 (mod pj) for some i and j and 1 <= k <= ei. - T. D. Noe (noe(AT)sspectra.com), Mar 25 2007
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CROSSREFS
| Complement of A051532.
Sequence in context: A000379 A176525 A065985 * A020739 A064466 A026286
Adjacent sequences: A060649 A060650 A060651 * A060653 A060654 A060655
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KEYWORD
| nonn
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AUTHOR
| Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 17 2001
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EXTENSIONS
| More terms from T. D. Noe (noe(AT)sspectra.com), Mar 11 2007
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