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A282777 Expansion of phi_{16, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}. 1
0, 1, 65538, 43046724, 4295098372, 152587890630, 2821196197512, 33232930569608, 281483566907400, 1853020317992013, 10000305176108940, 45949729863572172, 184889914172333328, 665416609183179854, 2178019803670969104, 6568408813691796120 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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

REFERENCES

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

LINKS

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

FORMULA

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.

MATHEMATICA

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

PROG

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

CROSSREFS

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).

Sequence in context: A036094 A133865 A194185 * A096555 A258533 A258526

Adjacent sequences:  A282774 A282775 A282776 * A282778 A282779 A282780

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, Feb 21 2017

STATUS

approved

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Last modified October 18 08:50 EDT 2018. Contains 316312 sequences. (Running on oeis4.)