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A057731
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Table T(n,k) giving number of elements of order k in symmetric group S_n, n >= 1, 1<=k<=g(n), where g(n) = A000793(n) is Landau's function..
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3
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1, 1, 1, 1, 3, 2, 1, 9, 8, 6, 1, 25, 20, 30, 24, 20, 1, 75, 80, 180, 144, 240, 1, 231, 350, 840, 504, 1470, 720, 0, 0, 504, 0, 420, 1, 763, 1232, 5460, 1344, 10640, 5760, 5040, 0, 4032, 0, 3360, 0, 0, 2688, 1, 2619, 5768, 30996, 3024, 83160, 25920, 45360, 40320, 27216, 0, 30240, 0, 25920, 24192, 0, 0, 0, 0, 18144
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Every row for n >= 7 contains zeros. Landau's function quickly becomes > 2*n, and there is always a prime between n and 2*n. T(n,p) = 0 for such a prime p. - Franklin T. Adams-Watters, Oct 25 2011.
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FORMULA
| Sum_{k=1...g(n)} T(n,k)*k = A060014(n) where g(n)= A000793(n) is Landau's function.
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EXAMPLE
| 1; 1,1; 1,3,2; 1,9,8,6; 1,25,20,30,24,20; ...
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MATHEMATICA
| Table[Distribution[Apply[LCM, Map[Length, Map[ToCycles, Permutations[n]], {2}], 1], Range[Max[Apply[LCM, Partitions[n], 1]]]], {n, 1, 8}]//Grid
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PROG
| (MAGMA) {* Order(g) : g in Sym(6) *};
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CROSSREFS
| Cf. A054522 (for cyclic group), A057740 (alternating group), A057741 (dihedral group).
Sequence in context: A193918 A155788 A108073 * A126074 A108916 A119421
Adjacent sequences: A057728 A057729 A057730 * A057732 A057733 A057734
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KEYWORD
| nonn,tabf,easy,nice
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AUTHOR
| Roger CUCULIERE (cuculier(AT)imaginet.fr), Oct 29 2000
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EXTENSIONS
| More terms from N. J. A. Sloane (njas(AT)research.att.com), Nov 01 2000
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