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A060828
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Size of the Sylow 3-subgroup of the symmetric group S_n.
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11
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1, 1, 1, 3, 3, 3, 9, 9, 9, 81, 81, 81, 243, 243, 243, 729, 729, 729, 6561, 6561, 6561, 19683, 19683, 19683, 59049, 59049, 59049, 1594323, 1594323, 1594323, 4782969, 4782969, 4782969, 14348907, 14348907, 14348907, 129140163, 129140163, 129140163, 387420489
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OFFSET
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0,4
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LINKS
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Tyler Ball, Tom Edgar, and Daniel Juda, Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
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FORMULA
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a(n) = 3^A054861(n) = 3^(floor(n/3) + floor(n/9) + floor(n/27) + floor(n/81) + ...).
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EXAMPLE
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a(3) = 3 because in S_3 the Sylow 3-subgroup is the subgroup generated by the 3-cycles (123) and (132), its order is 3.
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MATHEMATICA
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(* By the formula: *) Table[3^IntegerExponent[n!, 3], {n, 0, 40}] (* Bruno Berselli, Aug 05 2013 *)
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PROG
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(PARI) for (n=0, 200, s=0; d=3; while (n>=d, s+=n\d; d*=3); write("b060828.txt", n, " ", 3^s)) \\ Harry J. Smith, Jul 12 2009
(Sage)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 30 2001
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EXTENSIONS
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STATUS
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approved
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