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%I #23 Oct 30 2023 01:45:25
%S 0,1,16386,4782972,268468228,6103515630,78373779192,678223072856,
%T 4398583447560,22876806803877,100012207113180,379749833583252,
%U 1284076017413616,3937376385699302,11113363271818416,29192944359852360,72066391204823056,168377826559400946
%N Expansion of phi_{14, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
%C Multiplicative because A013961 is. - _Andrew Howroyd_, Jul 25 2018
%H Seiichi Manyama, <a href="/A282597/b282597.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = n*A013961(n) for n > 0.
%F a(n) = (3*A282012(n) + 4*A282287(n) - 7*A282596(n))/144.
%F Sum_{k=1..n} a(k) ~ zeta(14) * n^15 / 15. - _Amiram Eldar_, Sep 06 2023
%F From _Amiram Eldar_, Oct 30 2023: (Start)
%F Multiplicative with a(p^e) = p^e * (p^(13*e+13)-1)/(p^13-1).
%F Dirichlet g.f.: zeta(s-1)*zeta(s-14). (End)
%t Table[n * DivisorSigma[13, n], {n, 0, 17}] (* _Amiram Eldar_, Sep 06 2023 *)
%o (PARI) a(n) = if(n < 1, 0, n*sigma(n, 13)) \\ _Andrew Howroyd_, Jul 25 2018
%Y 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}).
%Y Cf. A282012 (E_4^4), A282287 (E_4*E_6^2), A282596 (E_2*E_4^2*E_6).
%Y Cf. A013672.
%K nonn,easy,mult
%O 0,3
%A _Seiichi Manyama_, Feb 19 2017
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