cp's OEIS Frontend

A068023 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=6.

%I A068023 #10 Nov 04 2016 09:54:13
%S A068023 1,127,1093,10795,19531,164809,137257,788035,896260,2745247,1948717,
%T A068023 15172249,5229043,18728221,22858948,53743987,25646167,142560946,
%U A068023 49659541,244930015,157475284,258931921,154764793,1151073625,317886556
%N A068023 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=6.
%F A068023 1/6!*(sigma[1](n)^6 + 15*sigma[1](n)^4*sigma[2](n) + 40*sigma[1](n)^3*sigma[3](n) + 45*sigma[1](n)^2*sigma[2](n)^2 + 90*sigma[1](n)^2*sigma[4](n) + 120*sigma[1](n)*sigma[2](n)*sigma[3](n) + 15*sigma[2](n)^3 + 144*sigma[1](n)*sigma[5](n) + 90*sigma[2](n)*sigma[4](n) + 40*sigma[3](n)^2 + 120*sigma[6](n)).
%F A068023 Agrees with A038994 at n = 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23... - _Ralf Stephan_, Mar 09 2004
%t A068023 CIP6 = CycleIndexPolynomial[SymmetricGroup[6], Array[x, 6]]; a[n_] := CIP6 /. x[k_] -> DivisorSigma[k, n]; Array[a, 25] (* _Jean-François Alcover_, Nov 04 2016 *)
%Y A068023 Cf. A067692, A068020-A068022, A068024-A068027, A000203, A001157-A001160, A013954.
%K A068023 nonn
%O A068023 1,2
%A A068023 _Vladeta Jovovic_, Feb 08 2002