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A277566 Irregular table by rows: Orders of subgroups of the symmetric group S_n.

%I A277566 #35 Nov 29 2016 10:55:13
%S A277566 1,1,2,1,2,3,6,1,2,3,4,6,8,12,24,1,2,3,4,5,6,8,10,12,20,24,60,120,1,2,
%T A277566 3,4,5,6,8,9,10,12,16,18,20,24,36,48,60,72,120,360,720,1,2,3,4,5,6,7,
%U A277566 8,9,10,12,14,16,18,20,21,24,36,40,42,48,60,72,120,144,168,240,360,720,2520,5040,1,2,3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,30,32,36,40,42,48,56,60,64,72,96,120,128,144,168,180,192,240,288,336,360,384,576,720,1152,1344,1440,2520,5040,20160,40320
%N A277566 Irregular table by rows: Orders of subgroups of the symmetric group S_n.
%C A277566 Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself).
%H A277566 Charles R Greathouse IV, <a href="/A277566/b277566.txt">Rows n = 1..12 of table, flattened</a>
%H A277566 Götz Pfeiffer, <a href="http://schmidt.nuigalway.ie/subgroups">Numbers of subgroups of various families of groups</a>
%e A277566 1;
%e A277566 1, 2;
%e A277566 1, 2, 3, 6;
%e A277566 1, 2, 3, 4, 6, 8, 12, 24;
%e A277566 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120;
%e A277566 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720;
%e A277566 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 21, 24, 36, 40, 42, 48, 60, 72, 120, 144, 168, 240, 360, 720, 2520, 5040;
%e A277566 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 24, 30, 32, 36, 40, 42, 48, 56, 60, 64, 72, 96, 120, 128, 144, 168, 180, 192, 240, 288, 336, 360, 384, 576, 720, 1152, 1344, 1440, 2520, 5040, 20160, 40320;
%o A277566 (GAP) LoadPackage("sonata");
%o A277566 a := function(n)
%o A277566   return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size)));
%o A277566 end;; # _Charles R Greathouse IV_, Nov 28 2016
%Y A277566 Row lengths are given by A218913.
%Y A277566 See A243748 for a closely related sequence.
%K A277566 nonn,tabf
%O A277566 1,3
%A A277566 _Charles R Greathouse IV_, Nov 28 2016