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%I #31 May 13 2023 23:51:08
%S 16,36,40,104,232,296,351,424,488,808,872,1125,1192,1197,1256,1384,
%T 1448,1576,1755,1832,2152,2216,2223,2331,2344,2536,2625,2792,2984,
%U 3112,3176,3368,3688,3861,4072,4328,4329,4456,4599,4875,4904,5115,5187,5224,5288,5301
%N Numbers m such that there are precisely 14 groups of order m.
%H Muniru A Asiru, <a href="/A294155/b294155.txt">Table of n, a(n) for n = 1..377</a>
%H H. U. Besche, B. Eick and E. A. O'Brien. <a href="http://www.icm.tu-bs.de/ag_algebra/software/small/">The Small Groups Library</a>
%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e For m = 16, the 14 groups of order 16 are C16, C4 x C4, (C4 x C2) : C2, C4 : C4, C8 x C2, C8 : C2, D16, QD16, Q16, C4 x C2 x C2, C2 x D8, C2 x Q8, (C4 x C2) : C2, C2 x C2 x C2 x C2 and for n = 36 the 14 groups of order 36 are C9 : C4, C36, (C2 x C2) : C9, D36, C18 x C2, C3 x (C3 : C4), (C3 x C3) : C4, C12 x C3, (C3 x C3) : C4, S3 x S3, C3 x A4, C6 x S3, C2 x ((C3 x C3) : C2), C6 x C6 where C, D, Q mean Cyclic group, Dihedral group, Quaternion group of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semi-direct products respectively.
%o (GAP) A294155 := Filtered([1..2015], n -> NumberSmallGroups(n) = 14);
%Y Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), A054396 (k=4), A054397 (k=5), A135850 (k=6), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), this sequence (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).
%K nonn
%O 1,1
%A _Muniru A Asiru_, Oct 24 2017
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