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A054397
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Numbers m such that there are precisely 5 groups of order m.
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27
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8, 12, 18, 20, 27, 50, 52, 68, 98, 116, 125, 135, 148, 164, 171, 212, 242, 244, 273, 292, 297, 333, 338, 343, 356, 388, 399, 404, 436, 452, 459, 548, 578, 596, 621, 628, 651, 657, 692, 722, 724, 741, 772, 777, 783, 788, 825, 855, 875, 916, 932, 964, 981
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OFFSET
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1,1
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COMMENTS
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For m = 2*p^2 (p prime), there are precisely 5 groups of order m, so A079704 and A143928 (p odd prime) are two subsequences. - Bernard Schott, Dec 10 2021
For m = p^3, p prime, there are also 5 groups of order m, so A030078, where these groups are described, is another subsequence. - Bernard Schott, Dec 11 2021
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LINKS
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Muniru A Asiru, Table of n, a(n) for n = 1..120 [a(109)-a(113) corrected by Georg Fischer, Mar 18 2022]
H. U. Besche, B. Eick and E. A. O'Brien, The Small Groups Library
Gordon Royle, Numbers of Small Groups
Index entries for sequences related to groups
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FORMULA
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Sequence is { k | A000001(k) = 5 }. - Muniru A Asiru, Nov 03 2017
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EXAMPLE
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For m = 8, the 5 groups of order 8 are C8, C4 x C2, D8, Q8, C2 x C2 x C2 and for m = 12 the 5 groups of order 12 are C3 : C4, C12, A4, D12, C6 x C2 where C, D, Q mean cyclic, dihedral, quaternion groups of the stated order and A is the alternating group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - Muniru A Asiru, Nov 03 2017
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MATHEMATICA
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Select[Range[10^4], FiniteGroupCount[#] == 5 &] (* Robert Price, May 23 2019 *)
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PROG
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(GAP) A054397 := Filtered([1..2015], n -> NumberSmallGroups(n) = 5); # Muniru A Asiru, Nov 03 2017
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CROSSREFS
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Cf. A000001, A003277, A030078, A054395, A054396, A055561, A054397, A079704, A135850, A143928.
Sequence in context: A228056 A187042 A285508 * A075818 A090738 A085103
Adjacent sequences: A054394 A054395 A054396 * A054398 A054399 A054400
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, May 21 2000
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EXTENSIONS
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More terms from Christian G. Bower, May 25 2000
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STATUS
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approved
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