cp's OEIS Frontend

A068022 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=5.

%I A068022 #7 Nov 04 2016 09:54:23
%S A068022 1,63,364,2667,3906,26964,19608,97155,99463,271278,177156,1228836,
%T A068022 402234,1324008,1520784,3309747,1508598,7746453,2613660,12021702,
%U A068022 7487424,11661372,6728904,46371780,12714681,26297334,25095280,57926792
%N A068022 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=5.
%F A068022 1/5!*(sigma[1](n)^5 + 10*sigma[1](n)^3*sigma[2](n) + 20*sigma[1](n)^2*sigma[3](n) + 15*sigma[1](n)*sigma[2](n)^2 + 30*sigma[1](n)*sigma[4](n) + 20*sigma[2](n)*sigma[3](n) + 24*sigma[5](n)).
%t A068022 CIP5 = CycleIndexPolynomial[SymmetricGroup[5], Array[x, 5]]; a[n_] := CIP5 /. x[k_] -> DivisorSigma[k, n]; Array[a, 28] (* _Jean-François Alcover_, Nov 04 2016 *)
%Y A068022 Cf. A067692, A068020, A068021, A068023-A068027, A000203, A001157-A001160.
%K A068022 nonn
%O A068022 1,2
%A A068022 _Vladeta Jovovic_, Feb 08 2002