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A292896 Numbers m such that there are precisely 13 groups of order m.

%I A292896 #52 May 13 2023 23:51:03
%S A292896 56,60,150,189,441,726,837,945,1012,1161,1204,1521,1575,1647,1734,
%T A292896 1809,1988,2079,2133,2205,2366,2619,2781,2925,2948,3174,3213,3556,
%U A292896 3610,3753,4077,4239,4324,4347,4851,5046,5211,5697,5805,5908,6021,6183,6507,6692,7479,7497,7605,7623,7641,7749,8410,8451
%N A292896 Numbers m such that there are precisely 13 groups of order m.
%H A292896 Muniru A Asiru, <a href="/A292896/b292896.txt">Table of n, a(n) for n = 1..273</a>
%H A292896 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A292896 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 A292896 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%e A292896 The 13 groups of order 56 have the following structure C7 : C8, C56, C7 : Q8, C4 x D14, D56, C2 x (C7 : C4), (C14 x C2) : C2, C28 x C2, C7 x D8, C7 x Q8, (C2 x C2 x C2) : C7, C2 x C2 x D14, C14 x C2 x C2 where C, D and Q mean Cyclic group, Dihedral group and Quarternion group of the stated order. The symbols x and : mean direct and semidirect products respectively.
%o A292896 (GAP) A292896 := Filtered([1..2015], n -> NumberSmallGroups(n) = 13);
%Y A292896 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), this sequence (k=13), A294155 (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).
%K A292896 nonn
%O A292896 1,1
%A A292896 _Muniru A Asiru_, Oct 23 2017
%E A292896 More terms from _Muniru A Asiru_, Nov 18 2017