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 A111918 Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^3)). 6
 1, 9, 89, 721, 18601, 2089, 103961, 832913, 68093153, 68347169, 8320810649, 8331482849, 1414167788681, 1416817979081, 1421435199689, 11373510649537, 3295255574810593, 366551352989977, 132591913780524097, 132652127531625601 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Denominator of x(n) = A111919(n); x(n) = a(n)/A111919(n) ---> Pi*Pi/7 = 6*zeta(2)/7. REFERENCES G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50. LINKS Robert Israel, Table of n, a(n) for n = 1..1150 Eric Weisstein's World of Mathematics, Odd Part Eric Weisstein's World of Mathematics, Riemann Zeta Function zeta(2) EXAMPLE a(50) = 429245027972423430658635002176171233144054521, A111919(50) = 307330458857514095936081844184308729630720000: x(50) = a(50)/A111919(50) = 1.39668..., x(50)*7/6 = 1.62946.... MAPLE S:= 0: Res:= NULL: for k from 1 to 25 do S:= S + 1/k^2/2^padic:-ordp(k, 2); Res:= Res, numer(S) od: Res; # Robert Israel, Jan 13 2020 MATHEMATICA oddPart[n_] := n/2^IntegerExponent[n, 2]; x[n_] := Sum[oddPart[k]/k^3, {k, 1, n}]; a[n_] := Numerator[x[n]]; Array[a, 20] (* Jean-François Alcover, Dec 13 2021 *) PROG (Magma) val:=func; [Numerator(&+[val(k)/(k^3):k in [1..n]]):n in [1..20]]; // Marius A. Burtea, Jan 13 2020 CROSSREFS Cf. A000265, A013661, A111919, A111929, A111920, A111922. Sequence in context: A175371 A291893 A217321 * A064616 A133486 A224760 Adjacent sequences: A111915 A111916 A111917 * A111919 A111920 A111921 KEYWORD nonn,frac AUTHOR Reinhard Zumkeller, Aug 21 2005 STATUS approved

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Last modified December 5 19:57 EST 2022. Contains 358588 sequences. (Running on oeis4.)