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A295161
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Numbers n such that there are precisely 16 groups of order n.
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6
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100, 126, 234, 405, 550, 558, 676, 774, 812, 1098, 1156, 1206, 1218, 1422, 1550, 1746, 1854, 2050, 2502, 2530, 2718, 2826, 2842, 2943, 2982, 3050, 3164, 3364, 3474, 3550, 3798, 3875, 3916, 4014, 4122, 4134, 4214, 4275, 4338, 4401, 4746, 4986, 5094, 5476, 5516, 5566, 5634, 5958, 6066, 6282
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history;
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OFFSET
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1,1
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LINKS
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Muniru A Asiru, Table of n, a(n) for n = 1..339
H. U. Besche, B. Eick and E. A. O'Brien. A Millennium Project: Constructing Small Groups, Internat. J. Algebra and Computation, 12 (2002), 623-644.
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) = 16 }.
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EXAMPLE
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For n = 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.
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PROG
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(GAP) A295161:=Filtered([1..2015], n->NumberSmallGroups(n)=16);
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CROSSREFS
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Cf. A000001, A003277, A054395, A054396, A054397, A055561, A135850, A249550, A249551, A249552, A249553, A249554, A249555, A292896, A294155, A294156, A294949.
Sequence in context: A037139 A109881 A292275 * A127336 A045211 A244391
Adjacent sequences: A295158 A295159 A295160 * A295162 A295163 A295164
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KEYWORD
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nonn
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AUTHOR
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Muniru A Asiru, Nov 15 2017
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STATUS
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approved
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