|
%I #12 Nov 04 2016 09:22:43
%S 1,15,40,155,156,672,400,1395,1210,2520,1464,7280,2380,6336,6600,
%T 11811,5220,21030,7240,26880,16672,22752,12720,66960,20306,36792,
%U 33880,67040,25260,119592,30784,97155,60144,80136,64080,230966,52060,110880,97384
%N 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=3.
%F 1/3!*(sigma[1](n)^3 + 3*sigma[1](n)*sigma[2](n) + 2*sigma[3](n)).
%F Sum_{r|n, s|n, t|n, r<=s<=t} r*s*t.
%t a[n_] := 1/3!*(DivisorSigma[1, n]^3 + 3*DivisorSigma[1, n]*DivisorSigma[2, n] + 2*DivisorSigma[3, n]); Table[a[n], {n, 1, 39}] (* _Jean-François Alcover_, Dec 12 2011, after given formula *)
%t CIP3 = CycleIndexPolynomial[SymmetricGroup[3], Array[x, 3]]; a[n_] := CIP3 /. x[k_] -> DivisorSigma[k, n]; Array[a, 39] (* _Jean-François Alcover_, Nov 04 2016 *)
%Y Cf. A067692, A068021-A068027, A000203, A001157, A001158.
%K nonn
%O 1,2
%A _Vladeta Jovovic_, Feb 08 2002
|
