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A282597
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Expansion of phi_{14, 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, 16386, 4782972, 268468228, 6103515630, 78373779192, 678223072856, 4398583447560, 22876806803877, 100012207113180, 379749833583252, 1284076017413616, 3937376385699302, 11113363271818416, 29192944359852360, 72066391204823056, 168377826559400946
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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(14) * n^15 / 15. - Amiram Eldar, Sep 06 2023
Multiplicative with a(p^e) = p^e * (p^(13*e+13)-1)/(p^13-1).
Dirichlet g.f.: zeta(s-1)*zeta(s-14). (End)
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MATHEMATICA
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Table[n * DivisorSigma[13, n], {n, 0, 17}] (* Amiram Eldar, Sep 06 2023 *)
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PROG
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(PARI) a(n) = if(n < 1, 0, n*sigma(n, 13)) \\ 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}, A282548 (phi_{12, 1}), this sequence (phi_{14, 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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