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 A054397 Numbers m such that there are precisely 5 groups of order m. 27
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS 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 FORMULA Sequence is { k | A000001(k) = 5 }. - Muniru A Asiru, Nov 03 2017 EXAMPLE 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 MATHEMATICA Select[Range[10^4], FiniteGroupCount[#] == 5 &] (* Robert Price, May 23 2019 *) PROG (GAP) A054397 := Filtered([1..2015], n -> NumberSmallGroups(n) = 5); # Muniru A Asiru, Nov 03 2017 CROSSREFS 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 KEYWORD nonn AUTHOR N. J. A. Sloane, May 21 2000 EXTENSIONS More terms from Christian G. Bower, May 25 2000 STATUS approved

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Last modified March 27 18:55 EDT 2023. Contains 361575 sequences. (Running on oeis4.)