A249551 Numbers m such that there are precisely 8 groups of order m.

510, 690, 870, 910, 1122, 1190, 1330, 1395, 1410, 1590, 1610, 1770, 1914, 2002, 2210, 2346, 2470, 2490, 2590, 2618, 2670, 2706, 2745, 2926, 2958, 2990, 3094, 3102, 3210, 3230, 3290, 3390, 3458, 3465, 3498, 3710, 3770, 3894, 3910, 4002, 4110, 4130, 4182, 4186, 4370, 4470

Offset: 1

Author

N. J. A. Sloane, Nov 01 2014

Keywords

• nonn

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..1064
• H. U. Besche, B. Eick and E. A. O'Brien, Numbers of isomorphism types of finite groups of given order
• 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), this sequence (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

GAP

A249551 := Filtered([1..2015], n -> NumberSmallGroups(n) = 8); # Muniru A Asiru, Oct 18 2017

Mathematica

Select[Range[10^4], FiniteGroupCount[#] == 8 &] (* A current limit in Mathematica is such that some orders >2047 may not be evaluated.*) (* Robert Price, May 24 2019 *)

Extensions

a(15)-a(16) from Muniru A Asiru, Oct 18 2017

More terms from Michael De Vlieger, Oct 18 2017

Missing terms added by Andrey Zabolotskiy, Oct 27 2017