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.

1, 127, 1093, 10795, 19531, 164809, 137257, 788035, 896260, 2745247, 1948717, 15172249, 5229043, 18728221, 22858948, 53743987, 25646167, 142560946, 49659541, 244930015, 157475284, 258931921, 154764793, 1151073625, 317886556

Offset

1,2

Links

Table of n, a(n) for n=1..25.

Formula

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)).

Agrees with A038994 at n = 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23... - Ralf Stephan, Mar 09 2004

Mathematica

CIP6 = CycleIndexPolynomial[SymmetricGroup[6], Array[x, 6]]; a[n_] := CIP6 /. x[k_] -> DivisorSigma[k, n]; Array[a, 25] (* Jean-François Alcover, Nov 04 2016 *)

Crossrefs

Cf. A067692, A068020-A068022, A068024-A068027, A000203, A001157-A001160, A013954.

Sequence in context: A225148 A160897 A038994 * A194257 A243529 A299718

Adjacent sequences: A068020 A068021 A068022 * A068024 A068025 A068026

Keyword

nonn

Author

Vladeta Jovovic, Feb 08 2002

Status

approved