A068020 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.

1, 15, 40, 155, 156, 672, 400, 1395, 1210, 2520, 1464, 7280, 2380, 6336, 6600, 11811, 5220, 21030, 7240, 26880, 16672, 22752, 12720, 66960, 20306, 36792, 33880, 67040, 25260, 119592, 30784, 97155, 60144, 80136, 64080, 230966, 52060, 110880, 97384

Offset

1,2

Links

Table of n, a(n) for n=1..39.

Formula

1/3!*(sigma[1](n)^3 + 3*sigma[1](n)*sigma[2](n) + 2*sigma[3](n)).

Sum_{r|n, s|n, t|n, r<=s<=t} r*s*t.

Mathematica

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 *)
CIP3 = CycleIndexPolynomial[SymmetricGroup[3], Array[x, 3]]; a[n_] := CIP3 /. x[k_] -> DivisorSigma[k, n]; Array[a, 39] (* Jean-François Alcover, Nov 04 2016 *)

Crossrefs

Cf. A067692, A068021-A068027, A000203, A001157, A001158.

Sequence in context: A223425 A175926 A038991 * A131991 A116042 A219378

Adjacent sequences: A068017 A068018 A068019 * A068021 A068022 A068023

Keyword

nonn

Author

Vladeta Jovovic, Feb 08 2002

Status

approved