A282060 -id:A282060 - cp's OEIS frontend

A289744 Coefficients in expansion of q*E'_8 where E_8 is the Eisenstein Series (A008410).

480, 123840, 3150720, 31704960, 187502400, 812885760, 2767107840, 8116473600, 20671878240, 48375619200, 102892268160, 208111357440, 391550752320, 713913822720, 1230765753600, 2077817249280, 3348363579840, 5333344585920, 8152110268800, 12384908524800

Offset: 1

Seiichi Manyama, Jul 11 2017

nonn

Seiichi Manyama, Table of n, a(n) for n = 1..10000

(-1)^(k/2)*q*E'_{k}: A076835 (k=2), A145094 (k=4), A145095 (k=6), this sequence (k=8), A289745 (k=10), A289746 (k=14).

Cf. A008410 (E_8), A013955, A282060, A289638.

Table[480*n*DivisorSigma[7, n], {n, 1, 20}] (* Jean-François Alcover, Feb 27 2018 *)

a(n) = 480 * n * sigma(n, 7); \\ Amiram Eldar, Jan 07 2025

a(n) = 480*A282060(n) = 480*n*A013955(n).

A282777 Expansion of phi_{16, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.

Original entry on oeis.org

0, 1, 65538, 43046724, 4295098372, 152587890630, 2821196197512, 33232930569608, 281483566907400, 1853020317992013, 10000305176108940, 45949729863572172, 184889914172333328, 665416609183179854, 2178019803670969104, 6568408813691796120

Offset: 0

Seiichi Manyama, Feb 21 2017

Multiplicative because A013963 is. - Andrew Howroyd, Jul 25 2018

George E. Andrews and Bruce C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012. See p. 212.

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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}).
Cf. A282546 (E_2*E_4^4), A282000 (E_4^3*E_6), A282547 (E_2*E_4*E_6^2), A282253 (E_6^3).
Cf. A013674.

Table[If[n==0, 0, n * DivisorSigma[15, n]], {n, 0, 15}] (* Indranil Ghosh, Mar 11 2017 *)

for(n=0, 15, print1(if(n==0, 0, n * sigma(n, 15)), ", ")) \\ Indranil Ghosh, Mar 11 2017

a(n) = n*A013963(n) for n > 0.
a(n) = (2156*A282546(n) - 4156*A282000(n) + 8000*A282547(n)/3 - 2000*A282253(n)/3)/16320.
Sum_{k=1..n} a(k) ~ zeta(16) * n^17 / 17. - Amiram Eldar, Sep 06 2023
From Amiram Eldar, Oct 30 2023: (Start)
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)

cp's OEIS Frontend

A289744 Coefficients in expansion of q*E'_8 where E_8 is the Eisenstein Series (A008410).

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