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A111930 Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).

%I A111930 #14 Feb 16 2025 08:32:58
%S A111930 1,4,12,48,240,240,1680,6720,20160,4032,44352,44352,576576,576576,
%T A111930 2882880,11531520,196035840,196035840,3724680960,3724680960,
%U A111930 3724680960,3724680960,85667662080,85667662080,428338310400,428338310400
%N A111930 Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).
%C A111930 Numerator of x(n) = A111929(n);
%C A111930 x(n) = A111929(n)/a(n) does not converge.
%D A111930 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.
%H A111930 Robert Israel, <a href="/A111930/b111930.txt">Table of n, a(n) for n = 1..2296</a>
%H A111930 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddPart.html">Odd Part</a>
%p A111930 map(denom, ListTools:-PartialSums([seq(1/k/2^padic:-ordp(k,2),k=1..100)])): # _Robert Israel_, Dec 28 2017
%t A111930 od[k_] := k/2^IntegerExponent[k, 2];
%t A111930 a[n_] := Sum[od[k]/k^2, {k, 1, n}] // Denominator;
%t A111930 Array[a, 25] (* _Jean-François Alcover_, Mar 08 2019 *)
%Y A111930 Cf. A000265, A111919, A111921, A111923.
%K A111930 nonn,frac
%O A111930 1,2
%A A111930 _Reinhard Zumkeller_, Aug 21 2005