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A282781
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Expansion of phi_{8, 3}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
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1
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0, 1, 264, 6588, 67648, 390750, 1739232, 5765144, 17318400, 43224597, 103158000, 214360212, 445665024, 815732918, 1521998016, 2574261000, 4433514496, 6975762354, 11411293608, 16983569900, 26433456000, 37980768672, 56591095968, 78310997448
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ zeta(6) * n^9 / 9. - Amiram Eldar, Sep 06 2023
Multiplicative with a(p^e) = p^(3*e) * (p^(5*e+5)-1)/(p^5-1).
Dirichlet g.f.: zeta(s-3)*zeta(s-8). (End)
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MATHEMATICA
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a[0]=0; a[n_]:=(n^3)*DivisorSigma[5, n]; Table[a[n], {n, 0, 23}] (* Indranil Ghosh, Feb 21 2017 *)
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PROG
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(PARI) a(n) = if (n==0, 0, n^3*sigma(n, 5)); \\ Michel Marcus, Feb 21 2017
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CROSSREFS
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Cf. A282211 (phi_{4, 3}), A282213 (phi_{6, 3}), this sequence (phi_{8, 3}).
Cf. A001160 (sigma_5(n)), A282050 (n*sigma_5(n)), A282751 (n^2*sigma_5(n)), this sequence (n^3*sigma_5(n)).
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KEYWORD
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nonn,easy,mult
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AUTHOR
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STATUS
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approved
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