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

Author

N. J. A. Sloane, Nov 01 2014

Keywords

• nonn

Examples

			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
		

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

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).

Programs

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

Formula

Sequence is { m | A000001(m) = 7 }. - Muniru A Asiru, Nov 11 2017

Extensions

More terms from Muniru A Asiru, Oct 22 2017

Missing terms added by Muniru A Asiru, Nov 12 2017