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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
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.
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
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.)