A249550 Numbers m such that there are precisely 7 groups of order m.

375, 605, 903, 1705, 2255, 2601, 2667, 3081, 3355, 3905, 3993, 4235, 4431, 4515, 4805, 5555, 6123, 6355, 6375, 6765, 7077, 7205, 7865, 7917, 7959, 8305, 8405, 8625, 8841, 9455, 9723, 9933, 9955, 10285, 10505, 10875, 11005, 11487, 11495, 11571, 11605, 11715, 11935, 12207, 12505, 13005, 13053, 13251, 13255, 13335, 13805, 14133

Offset

1,1

Links

Muniru A Asiru, Table of n, a(n) for n = 1..198

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) = 7 }. - Muniru A Asiru, Nov 11 2017

Example

For m = 375, the 7 groups are C375, ((C5 x C5) : C5) : C3, C75 x C5, C3 x ((C5 x C5) : C5), C3 x (C25 : C5), C5 x ((C5 x C5) : C3), C15 x C5 x C5 and for n = 605 the 7 groups are C121 : C5, C605, C11 x (C11 : C5), (C11 x C11) : C5, (C11 x C11) : C5, (C11 x C11) : C5, C55 x C11, where C means Cyclic group and the symbols x and : mean direct and semidirect products respectively. - Muniru A Asiru, Nov 11 2017

Mathematica

Warning: The Mma command Select[Range[10^5], FiniteGroupCount[#]==7 &]  gives wrong answers, since FiniteGroupCount[2601] does not return 7. - N. J. A. Sloane, Apr 11 2020

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), this sequence (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), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

Sequence in context: A269113 A268751 A369663 * A045200 A252071 A247263

Adjacent sequences: A249547 A249548 A249549 * A249551 A249552 A249553

Keyword

nonn

Author

N. J. A. Sloane, Nov 01 2014

Extensions

More terms from Muniru A Asiru, Oct 22 2017

Missing terms added by Muniru A Asiru, Nov 12 2017

Status

approved