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 A295161 Numbers m such that there are precisely 16 groups of order m. 20
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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 FORMULA Sequence is { m | A000001(m) = 16 }. EXAMPLE 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. PROG (GAP) A295161:=Filtered([1..2015], n->NumberSmallGroups(n)=16); CROSSREFS 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). Sequence in context: A037139 A109881 A292275 * A127336 A045211 A244391 Adjacent sequences: A295158 A295159 A295160 * A295162 A295163 A295164 KEYWORD nonn AUTHOR Muniru A Asiru, Nov 15 2017 STATUS approved

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Last modified December 9 17:09 EST 2023. Contains 367693 sequences. (Running on oeis4.)