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A282777
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Expansion of phi_{16, 1}(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, 65538, 43046724, 4295098372, 152587890630, 2821196197512, 33232930569608, 281483566907400, 1853020317992013, 10000305176108940, 45949729863572172, 184889914172333328, 665416609183179854, 2178019803670969104, 6568408813691796120
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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George E. Andrews and Bruce C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012. See p. 212.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ zeta(16) * n^17 / 17. - Amiram Eldar, Sep 06 2023
Multiplicative with a(p^e) = p^e * (p^(15*e+15)-1)/(p^15-1).
Dirichlet g.f.: zeta(s-1)*zeta(s-16). (End)
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MATHEMATICA
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Table[If[n==0, 0, n * DivisorSigma[15, n]], {n, 0, 15}] (* Indranil Ghosh, Mar 11 2017 *)
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PROG
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(PARI) for(n=0, 15, print1(if(n==0, 0, n * sigma(n, 15)), ", ")) \\ Indranil Ghosh, Mar 11 2017
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CROSSREFS
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Cf. A064987 (phi_{2, 1}), A281372 (phi_{4, 1}), A282050 (phi_{6, 1}), A282060 (phi_{8, 1}), A282254 (phi_{10, 1}, A282548 (phi_{12, 1}), A282597 (phi_{14, 1}), this sequence (phi_{16, 1}).
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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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