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%I #35 Nov 29 2016 10:55:13
%S 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 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 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 Irregular table by rows: Orders of subgroups of the symmetric group S_n.
%C Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself).
%H Charles R Greathouse IV, <a href="/A277566/b277566.txt">Rows n = 1..12 of table, flattened</a>
%H Götz Pfeiffer, <a href="http://schmidt.nuigalway.ie/subgroups">Numbers of subgroups of various families of groups</a>
%e 1;
%e 1, 2;
%e 1, 2, 3, 6;
%e 1, 2, 3, 4, 6, 8, 12, 24;
%e 1, 2, 3, 4, 5, 6, 8, 10, 12, 20, 24, 60, 120;
%e 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 16, 18, 20, 24, 36, 48, 60, 72, 120, 360, 720;
%e 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 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 (GAP) LoadPackage("sonata");
%o a := function(n)
%o return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size)));
%o end;; # _Charles R Greathouse IV_, Nov 28 2016
%Y Row lengths are given by A218913.
%Y See A243748 for a closely related sequence.
%K nonn,tabf
%O 1,3
%A _Charles R Greathouse IV_, Nov 28 2016
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