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A277566
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Irregular table by rows: Orders of subgroups of the symmetric group S_n.
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2
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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
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1,3
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COMMENTS
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Each row begins with 1 (the order of the trivial group) and ends with n! (the order of S_n itself).
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LINKS
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EXAMPLE
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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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PROG
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(GAP) LoadPackage("sonata");
a := function(n)
return Length(Unique(Apply(Subgroups(SymmetricGroup(n)), Size)));
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CROSSREFS
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See A243748 for a closely related sequence.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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