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A284210
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Number of subgroups of order n of the symmetric group Sym(n) on n symbols.
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2
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1, 1, 1, 7, 6, 280, 120, 25335, 11200, 276696, 362880, 374838255, 39916800, 2414617920, 11721790080
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OFFSET
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1,4
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COMMENTS
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The diagonal of A243748 (once the 0's for non-divisors of n are filled in). - R. J. Mathar, Mar 30 2017
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LINKS
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FORMULA
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If n is prime, A284210(n) = (n-2)!.
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EXAMPLE
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The group Sym(4) contains 3 cyclic groups of order 4, 3 non-normal elementary abelian groups of order 4 and one normal group of order 4, so A284210(4) = 3 + 3 + 1 = 7.
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PROG
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(GAP) List([1..14], n -> Sum(List(Filtered(ConjugacyClassesSubgroups(SymmetricGroup(n)), c -> Size(Representative(c)) = n)), c -> Size(c)));
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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