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A295161 Numbers m such that there are precisely 16 groups of order m.

%I A295161 #19 May 13 2023 23:51:20
%S A295161 100,126,234,405,550,558,676,774,812,1098,1156,1206,1218,1422,1550,
%T A295161 1746,1854,2050,2502,2530,2718,2826,2842,2943,2982,3050,3164,3364,
%U A295161 3474,3550,3798,3875,3916,4014,4122,4134,4214,4275,4338,4401,4746,4986,5094,5476,5516,5566,5634,5958,6066,6282
%N A295161 Numbers m such that there are precisely 16 groups of order m.
%H A295161 Muniru A Asiru, <a href="/A295161/b295161.txt">Table of n, a(n) for n = 1..339</a>
%H A295161 H. U. Besche, B. Eick and E. A. O'Brien. <a href="http://dx.doi.org/10.1142/S0218196702001115">A Millennium Project: Constructing Small Groups</a>, Internat. J. Algebra and Computation, 12 (2002), 623-644.
%H A295161 Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H A295161 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F A295161 Sequence is { m | A000001(m) = 16 }.
%e A295161 For m = 100, the 16 groups are C25 : C4, C100, C25 : C4, D100, C50 x C2, C5 x (C5 : C4), (C5 x C5) : C4, C20 x C5, C5 x (C5 : C4), (C5 x C5) : C4, (C5 x C5) : C4, (C5 x C5) : C4, D10 x D10, C10 x D10, C2 x ((C5 x C5) : C2), C10 x C10 where C, D mean Cyclic, Dihedral groups of the stated order and the symbols x and : mean direct and semidirect products respectively.
%o A295161 (GAP) A295161:=Filtered([1..2015],n->NumberSmallGroups(n)=16);
%Y A295161 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), A294155 (k=14), A294156 (k=15), this sequence (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).
%K A295161 nonn
%O A295161 1,1
%A A295161 _Muniru A Asiru_, Nov 15 2017