A068027 Z(S_m; sigma[1](n), sigma[2](n),..., sigma[m](n)) where Z(S_m; x_1,x_2,...,x_m) is the cycle index of the symmetric group S_m and sigma[k](n) is the sum of k-th powers of divisors of n; m=10.

1, 2047, 88573, 2794155, 12207031, 217414561, 329554457, 3269560515, 5883904390, 27757433067, 28531167061, 323579719281, 149346699503, 726383654349, 1158434219878, 3571013994483, 2141993519227, 15288525998824

Offset: 1

Author

Vladeta Jovovic, Feb 08 2002

Keywords

• nonn

Crossrefs

Cf. A067692, A068020-A068026, A000203, A001157-A001160, A013954-A013958.

Programs

Mathematica

CIP10 = CycleIndexPolynomial[SymmetricGroup[10], Array[x, 10]]; a[n_] := CIP10 /. x[k_] -> DivisorSigma[k, n]; Array[a, 18] (* Jean-François Alcover, Nov 04 2016 *)