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%I #23 Sep 08 2022 08:45:21
%S 1,8,72,576,14400,1600,78400,627200,50803200,50803200,6147187200,
%T 6147187200,1038874636800,1038874636800,1038874636800,8310997094400,
%U 2401878160281600,266875351142400,96342001762406400,96342001762406400
%N Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^3)).
%C Numerator of x(n) = A111918(n);
%C x(n) = A111918(n)/a(n) ---> Pi*Pi/7 = 6*zeta(2)/7.
%D G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.
%H Robert Israel, <a href="/A111919/b111919.txt">Table of n, a(n) for n = 1..1150</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddPart.html">Odd Part</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RiemannZetaFunctionZeta2.html">Riemann Zeta Function zeta(2)</a>
%p S:= 0: Res:= NULL:
%p for k from 1 to 25 do
%p S:= S + 1/k^2/2^padic:-ordp(k,2);
%p Res:= Res, denom(S);
%p od:
%p Res; # _Robert Israel_, Jan 13 2020
%t oddPart[n_] := n/2^IntegerExponent[n, 2];
%t x[n_] := Sum[oddPart[k]/k^3, {k, 1, n}];
%t a[n_] := Denominator[x[n]];
%t Array[a, 20] (* _Jean-François Alcover_, Dec 13 2021 *)
%o (Magma) val:=func<n|n/2^Valuation(n,2)>; [Denominator(&+[val(k)/(k^3):k in [1..n]]):n in [1..20]]; // _Marius A. Burtea_, Jan 13 2020
%Y Cf. A000265, A013661, A111918, A111930, A111921, A111923.
%K nonn,frac
%O 1,2
%A _Reinhard Zumkeller_, Aug 21 2005
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