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A068020
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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.
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8
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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.
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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}] (* From Jean-François Alcover, Dec 12 2011, after given formula *)
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CROSSREFS
| Cf. A067692, A068021-A068027, A000203, A001157, A001158.
Sequence in context: A160891 A175926 A038991 * A131991 A116042 A103003
Adjacent sequences: A068017 A068018 A068019 * A068021 A068022 A068023
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KEYWORD
| nonn
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AUTHOR
| Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 08 2002
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