cp's OEIS Frontend

A111929 Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).

%I A111929 #17 Feb 16 2025 08:32:58
%S A111929 1,5,19,79,443,463,3481,14029,44327,9067,103769,104693,1405361,
%T A111929 1425953,7321957,29332873,510190361,515635801,9993116059,10039674571,
%U A111929 10217040331,10301692171,240663600893,241109786633,1222682465581
%N A111929 Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).
%C A111929 Denominator of x(n) = A111930(n);
%C A111929 x(n) = a(n)/A111930(n) does not converge.
%D A111929 G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Eight, Chap. 1, Sect. 6, Problem 50.
%H A111929 Robert Israel, <a href="/A111929/b111929.txt">Table of n, a(n) for n = 1..2296</a>
%H A111929 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/OddPart.html">Odd Part</a>
%p A111929 map(numer, ListTools:-PartialSums([seq(1/k/2^padic:-ordp(k,2),k=1..100)])); # _Robert Israel_, Dec 28 2017
%t A111929 od[k_] := k/2^IntegerExponent[k, 2];
%t A111929 a[n_] := Sum[od[k]/k^2, {k, 1, n}] // Numerator;
%t A111929 Array[a, 25] (* _Jean-François Alcover_, Mar 08 2019 *)
%Y A111929 Cf. A000265, A111918, A111920, A111922, A111930.
%K A111929 nonn,frac
%O A111929 1,2
%A A111929 _Reinhard Zumkeller_, Aug 21 2005