cp's OEIS Frontend

A068021 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=4.

%I A068021 #7 Nov 04 2016 09:54:34
%S A068021 1,31,121,651,781,4333,2801,11811,11011,26481,16105,96957,30941,92613,
%T A068021 100771,200787,88741,412087,137561,579201,354923,520221,292561,
%U A068021 1812477,508431,993153,925771,2003477,732541,3996003,954305,3309747,2006851
%N A068021 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=4.
%F A068021 1/4!*(sigma[1](n)^4 + 6*sigma[1](n)^2*sigma[2](n) + 8*sigma[1](n)*sigma[3](n) + 3*sigma[2](n)^2 + 6*sigma[4](n)).
%t A068021 CIP4 = CycleIndexPolynomial[SymmetricGroup[4], Array[x, 4]]; a[n_] := CIP4 /. x[k_] -> DivisorSigma[k, n]; Array[a, 33] (* _Jean-François Alcover_, Nov 04 2016 *)
%Y A068021 Cf. A067692, A068020, A068022-A068027, A000203, A001157, A001158, A001159.
%K A068021 nonn
%O A068021 1,2
%A A068021 _Vladeta Jovovic_, Feb 08 2002