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 A281372 Coefficients in q-expansion of (E_2*E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively. 12
 0, 1, 18, 84, 292, 630, 1512, 2408, 4680, 6813, 11340, 14652, 24528, 28574, 43344, 52920, 74896, 83538, 122634, 130340, 183960, 202272, 263736, 279864, 393120, 393775, 514332, 551880, 703136, 707310, 952560, 923552, 1198368, 1230768, 1503684, 1517040, 1989396, 1874198, 2346120, 2400216, 2948400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The q-expansion of the square of this expression is given in A281371. Multiplicative because A001158 is. - Andrew Howroyd, Jul 23 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA a(n) = A145094(n)/240 for n > 0. - Seiichi Manyama, Feb 04 2017 G.f.: phi_{4, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}. - Seiichi Manyama, Feb 04 2017 a(n) = n*A001158(n) for n > 0. - Seiichi Manyama, Feb 18 2017 G.f.: x*f'(x), where f(x) = Sum_{k>=1} k^3*x^k/(1 - x^k). - Ilya Gutkovskiy, Aug 31 2017 MAPLE with(numtheory); M:=100; E := proc(k) local n, t1; global M; t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..M+1); series(t1, q, M+1); end; e2:=E(2); e4:=E(4); e6:=E(6); t1:=series((e2*e4-e6)/720, q, M+1); seriestolist(t1); MATHEMATICA Table[If[n==0, 0, n * DivisorSigma[3, n]], {n, 0, 40}] (* Indranil Ghosh, Mar 11 2017 *) terms = 41; Ei[n_] = 1-(2n/BernoulliB[n]) Sum[k^(n-1) x^k/(1-x^k), {k, terms}]; CoefficientList[(Ei[2] Ei[4] - Ei[6])/720 + O[x]^terms, x] (* Jean-François Alcover, Mar 01 2018 *) PROG (PARI) for(n=0, 40, print1(if(n==0, 0, n * sigma(n, 3)), ", ")) \\ Indranil Ghosh, Mar 11 2017 (MAGMA) [0] cat [n*DivisorSigma(3, n): n in [1..50]]; // Vincenzo Librandi, Mar 01 2018 CROSSREFS Cf. A001158, A006352, A004009, A013973, A145094, A281371. Sequence in context: A039358 A043961 A067984 * A124935 A126405 A250101 Adjacent sequences:  A281369 A281370 A281371 * A281373 A281374 A281375 KEYWORD nonn,mult AUTHOR N. J. A. Sloane, Feb 04 2017 STATUS approved

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Last modified April 7 13:55 EDT 2020. Contains 333305 sequences. (Running on oeis4.)