A181954 Weighted sum of all cyclic subgroups of prime order of the symmetric group S_n.

0, 2, 9, 30, 110, 450, 2457, 11774, 47910, 264630, 5565065, 56021922, 866143434, 9894742130, 78233264865, 470058202350, 24530748587102, 409761902222094, 10595012400106545, 160826238368038490, 1585844131838898330, 16787211702213659322, 1362379222505265018329

Offset: 1

Author

Olivier Gérard, Apr 03 2012

Keywords

• nonn

Comments

Sum of the orders of all subgroups of prime order in S_n.

Examples

			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.
		

Links

• Stephen A. Silver, Table of n, a(n) for n = 1..451

Crossrefs

Cf. A181955 (the alternating case).

Programs

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 *)

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

Formula

a(n) = A186202(n) + A214003(n).

Extensions

More terms from Stephen A. Silver, Feb 16 2013