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.

1, 63, 364, 2667, 3906, 26964, 19608, 97155, 99463, 271278, 177156, 1228836, 402234, 1324008, 1520784, 3309747, 1508598, 7746453, 2613660, 12021702, 7487424, 11661372, 6728904, 46371780, 12714681, 26297334, 25095280, 57926792

Offset

1,2

Links

Table of n, a(n) for n=1..28.

Formula

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)).

Mathematica

CIP5 = CycleIndexPolynomial[SymmetricGroup[5], Array[x, 5]]; a[n_] := CIP5 /. x[k_] -> DivisorSigma[k, n]; Array[a, 28] (* Jean-François Alcover, Nov 04 2016 *)

Crossrefs

Cf. A067692, A068020, A068021, A068023-A068027, A000203, A001157-A001160.

Sequence in context: A160895 A203556 A038993 * A131993 A251019 A251012

Adjacent sequences: A068019 A068020 A068021 * A068023 A068024 A068025

Keyword

nonn

Author

Vladeta Jovovic, Feb 08 2002

Status

approved