|
| |
|
|
A060828
|
|
Size of the Sylow 3-subgroup of the symmetric group S_n.
|
|
3
|
|
|
|
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
|
|
|
FORMULA
|
a(n) = 3^(A054861(n)) = 3^([n/3]+[n/9]+[n/27]+[n/81]+...).
|
|
|
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.
|
|
|
PROG
|
(PARI) { for (n=0, 200, s=0; d=3; while (n>=d, s+=n\d; d*=3); write("b060828.txt", n, " ", 3^s); ) } [From 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
|
| |
|
|
