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.
1, 31, 121, 651, 781, 4333, 2801, 11811, 11011, 26481, 16105, 96957, 30941, 92613, 100771, 200787, 88741, 412087, 137561, 579201, 354923, 520221, 292561, 1812477, 508431, 993153, 925771, 2003477, 732541, 3996003, 954305, 3309747, 2006851
Offset: 1
Keywords
Programs
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Mathematica
CIP4 = CycleIndexPolynomial[SymmetricGroup[4], Array[x, 4]]; a[n_] := CIP4 /. x[k_] -> DivisorSigma[k, n]; Array[a, 33] (* Jean-François Alcover, Nov 04 2016 *)
Formula
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)).