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%I #32 Dec 24 2016 21:29:42
%S 1,1,1,3,3,3,9,9,9,81,81,81,243,243,243,729,729,729,6561,6561,6561,
%T 19683,19683,19683,59049,59049,59049,1594323,1594323,1594323,4782969,
%U 4782969,4782969,14348907,14348907,14348907,129140163,129140163,129140163,387420489
%N Size of the Sylow 3-subgroup of the symmetric group S_n.
%H Harry J. Smith, <a href="/A060828/b060828.txt">Table of n, a(n) for n = 0..200</a>
%H Tyler Ball, Tom Edgar, and Daniel Juda, <a href="http://dx.doi.org/10.4169/math.mag.87.2.135">Dominance Orders, Generalized Binomial Coefficients, and Kummer's Theorem</a>, Mathematics Magazine, Vol. 87, No. 2, April 2014, pp. 135-143.
%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>
%F a(n) = 3^A054861(n) = 3^(floor(n/3) + floor(n/9) + floor(n/27) + floor(n/81) + ...).
%F a(n) = Product_{i=1..n} A038500(i). - _Tom Edgar_, Apr 30 2014
%F a(n) = 3^(n/2 + O(log n)). - _Charles R Greathouse IV_, Aug 05 2015
%e 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.
%t (* By the formula: *) Table[3^IntegerExponent[n!, 3], {n, 0, 40}] (* _Bruno Berselli_, Aug 05 2013 *)
%o (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
%o (Sage)
%o def A060828(n):
%o A004128 = lambda n: A004128(n//3) + n if n > 0 else 0
%o return 3^A004128(n//3)
%o [A060828(i) for i in (0..39)] # _Peter Luschny_, Nov 16 2012
%Y Cf. A054861, A060818.
%K nonn,easy
%O 0,4
%A Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 30 2001
%E More terms from _N. J. A. Sloane_, Jul 03 2008
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