A181949 Weighted sum of all cyclic subgroups of the Symmetric Group.

1, 3, 10, 43, 231, 1531, 11068, 89895, 820543, 8484871, 95647476, 1186289083, 15648402355, 221728356123, 3354790995676, 53999879550991, 936289020367263, 17163114699673615, 328827078340587148, 6630244432204704771, 139769193881466850051, 3092293682224076627683

Offset: 1

Author

Olivier Gérard, Apr 03 2012

Keywords

• nonn
• easy

Comments

Sum of the orders of all cyclic subgroups of the Sym_n.

The identity permutation is counted for each subgroup, i.e. A051625(n) times.

Each permutation is counted several times according to its conjugacy class.

Examples

			a(4) = 1*1 + 2*3 + 2*6 + 3*4 + 4*3 = 1+6+12+12+12 = 43.
		

Crossrefs

Cf. A000793, A051625, A074881.

Formula

a(n) = Sum_{k=1..A000793(n)} k*A074881(n, k). - Andrew Howroyd, Jul 02 2018

Extensions

a(9)-a(22) from Andrew Howroyd, Jul 02 2018