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Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).
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%I #13 Dec 25 2019 08:35:10

%S 1,4,12,48,240,240,1680,6720,20160,4032,44352,44352,576576,576576,

%T 2882880,11531520,196035840,196035840,3724680960,3724680960,

%U 3724680960,3724680960,85667662080,85667662080,428338310400,428338310400

%N Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).

%C Numerator of x(n) = A111929(n);

%C x(n) = A111929(n)/a(n) does not converge.

%D G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.

%H Robert Israel, <a href="/A111930/b111930.txt">Table of n, a(n) for n = 1..2296</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OddPart.html">Odd Part</a>

%p map(denom, ListTools:-PartialSums([seq(1/k/2^padic:-ordp(k,2),k=1..100)])): # _Robert Israel_, Dec 28 2017

%t od[k_] := k/2^IntegerExponent[k, 2];

%t a[n_] := Sum[od[k]/k^2, {k, 1, n}] // Denominator;

%t Array[a, 25] (* _Jean-François Alcover_, Mar 08 2019 *)

%Y Cf. A000265, A111919, A111921, A111923.

%K nonn,frac

%O 1,2

%A _Reinhard Zumkeller_, Aug 21 2005