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A060828 Size of the Sylow 3-subgroup of the symmetric group S_n. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..200

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.

FORMULA

a(n) = 3^A054861(n) = 3^([n/3]+[n/9]+[n/27]+[n/81]+ ...).

a(n) = prod_{i=1..n} A038500(i). - Tom Edgar, Apr 30 2014.

EXAMPLE

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.

MATHEMATICA

(* By the formula: *) Table[3^IntegerExponent[n!, 3], {n, 0, 40}] (* Bruno Berselli, Aug 05 2013 *)

PROG

(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)

def A060828(n):

    A004128 = lambda n: A004128(n//3) + n if n > 0 else 0

    return 3^A004128(n//3)

[A060828(i) for i in (0..39)]  # Peter Luschny, Nov 16 2012

CROSSREFS

Cf. A054861, A060818.

Sequence in context: A132171 A217645 A127975 * A161808 A188344 A217457

Adjacent sequences:  A060825 A060826 A060827 * A060829 A060830 A060831

KEYWORD

nonn

AUTHOR

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 30 2001

EXTENSIONS

More terms from N. J. A. Sloane, Jul 03 2008

STATUS

approved

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Last modified March 26 18:40 EDT 2015. Contains 255911 sequences.