A294155 Numbers m such that there are precisely 14 groups of order m.

16, 36, 40, 104, 232, 296, 351, 424, 488, 808, 872, 1125, 1192, 1197, 1256, 1384, 1448, 1576, 1755, 1832, 2152, 2216, 2223, 2331, 2344, 2536, 2625, 2792, 2984, 3112, 3176, 3368, 3688, 3861, 4072, 4328, 4329, 4456, 4599, 4875, 4904, 5115, 5187, 5224, 5288, 5301

Offset: 1

Author

Muniru A Asiru, Oct 24 2017

Keywords

• nonn

Examples

			For m = 16, the 14 groups of order 16 are C16, C4 x C4, (C4 x C2) : C2, C4 : C4, C8 x C2, C8 : C2, D16, QD16, Q16, C4 x C2 x C2, C2 x D8, C2 x Q8, (C4 x C2) : C2, C2 x C2 x C2 x C2  and for n = 36 the 14 groups of order 36 are C9 : C4, C36, (C2 x C2) : C9, D36, C18 x C2, C3 x (C3 : C4), (C3 x C3) : C4, C12 x C3, (C3 x C3) : C4, S3 x S3, C3 x A4, C6 x S3, C2 x ((C3 x C3) : C2), C6 x C6 where C, D, Q  mean Cyclic group, Dihedral group, Quaternion group of the stated order and S is the Symmetric group of the stated degree. The symbols x and : mean direct and semi-direct products respectively.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..377
• H. U. Besche, B. Eick and E. A. O'Brien. The Small Groups Library
• 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), A249550 (k=7), A249551 (k=8), A249552 (k=9), A249553 (k=10), A249554 (k=11), A249555 (k=12), A292896 (k=13), this sequence (k=14), A294156 (k=15), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).

Programs

GAP

A294155 := Filtered([1..2015], n -> NumberSmallGroups(n) = 14);