%I #45 May 13 2023 23:50:13
%S 28,30,44,63,66,70,76,92,102,117,124,130,138,154,170,172,174,182,188,
%T 190,230,236,238,246,266,268,275,279,282,284,286,290,315,316,318,322,
%U 332,354,370,374,387,412,418,426,428,430,434,442,465,470,494,495,498
%N Numbers m such that there are precisely 4 groups of order m.
%H Jorge R. F. F. Lopes, <a href="/A054396/b054396.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..369 from Muniru A Asiru).
%H H. U. Besche, B. Eick and E. A. O'Brien, <a href="http://www.icm.tu-bs.de/ag_algebra/software/small/">The Small Groups Library</a>
%H Gordon Royle, <a href="http://staffhome.ecm.uwa.edu.au/~00013890/remote/cubcay/">Numbers of Small Groups</a>
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F Sequence is { m | A000001(m) = 4 }. - _Muniru A Asiru_, Nov 04 2017
%e For m = 28, the 4 groups of order 8 are C7 : C4, C28, D28, C14 x C2 and for m = 30 the 4 groups of order 30 are C5 x S3, C3 x D10, D30, C30 where C, D mean cyclic, dihedral groups of the stated order and S is the symmetric group of the stated degree. The symbols x and : mean direct and semidirect products respectively. - _Muniru A Asiru_, Nov 04 2017
%t Select[Range[500], FiniteGroupCount[#] == 4 &] (* _Jean-François Alcover_, Dec 08 2017 *)
%o (GAP) A054396 := Filtered([1..2015], n -> NumberSmallGroups(n) = 4); # _Muniru A Asiru_, Nov 04 2017
%Y Cf. A000001. Cyclic numbers A003277. Numbers m such that there are precisely k groups of order m: A054395 (k=2), A055561 (k=3), this sequence (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), A295161 (k=16), A294949 (k=17), A298909 (k=18), A298910 (k=19), A298911 (k=20).
%K nonn
%O 1,1
%A _N. J. A. Sloane_, May 21 2000
%E More terms from _Christian G. Bower_, May 25 2000