

A277566


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


2



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, 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, 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
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OFFSET

1,3


COMMENTS

Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself).


LINKS

Charles R Greathouse IV, Rows n = 1..12 of table, flattened
Götz Pfeiffer, Numbers of subgroups of various families of groups


EXAMPLE

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, 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, 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;


PROG

(GAP) LoadPackage("sonata");
a := function(n)
return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size)));
end;; # Charles R Greathouse IV, Nov 28 2016


CROSSREFS

Row lengths are given by A218913.
See A243748 for a closely related sequence.
Sequence in context: A135938 A079210 A070861 * A261144 A106524 A323641
Adjacent sequences: A277563 A277564 A277565 * A277567 A277568 A277569


KEYWORD

nonn,tabf


AUTHOR

Charles R Greathouse IV, Nov 28 2016


STATUS

approved



