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A282548
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Expansion of phi_{12, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
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3
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0, 1, 4098, 531444, 16785412, 244140630, 2177857512, 13841287208, 68753047560, 282431130813, 1000488301740, 3138428376732, 8920506494928, 23298085122494, 56721594978384, 129747072969720, 281612482805776, 582622237229778, 1157402774071674
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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(12) * n^13 / 13. - Amiram Eldar, Sep 06 2023
Multiplicative with a(p^e) = p^e * (p^(11*e+11)-1)/(p^11-1).
Dirichlet g.f.: zeta(s-1)*zeta(s-12). (End)
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MATHEMATICA
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Table[n * DivisorSigma[11, n], {n, 0, 18}] (* Amiram Eldar, Sep 06 2023 *)
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PROG
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(PARI) a(n) = if(n < 1, 0, n*sigma(n, 11)) \\ Andrew Howroyd, Jul 25 2018
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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}, this sequence (phi_{12, 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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