OFFSET
1,2
COMMENTS
Sum of the orders of all subgroups of prime order in S_n.
LINKS
Stephen A. Silver, Table of n, a(n) for n = 1..451
EXAMPLE
The symmetric group S_3 has one subgroup of order 3 and three subgroups of order 2, and no other subgroups of prime order. So a(3) = 3 + 2 + 2 + 2 = 9.
MATHEMATICA
a[n_] := Sum[If[PrimeQ[p], Sum[n!/(k!*(n-k*p)!*p^k), {k, 1, n/p}]*p/(p-1), 0], {p, 2, n}];
Array[a, 24] (* Jean-François Alcover, Jul 06 2018, after Andrew Howroyd *)
PROG
(PARI) a(n)={sum(p=2, n, if(isprime(p), sum(k=1, n\p, n!/(k!*(n-k*p)!*p^k))*p/(p-1)))} \\ Andrew Howroyd, Jul 03 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Olivier Gérard, Apr 03 2012
EXTENSIONS
More terms from Stephen A. Silver, Feb 16 2013
STATUS
approved