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

1, 5, 19, 79, 443, 463, 3481, 14029, 44327, 9067, 103769, 104693, 1405361, 1425953, 7321957, 29332873, 510190361, 515635801, 9993116059, 10039674571, 10217040331, 10301692171, 240663600893, 241109786633, 1222682465581

Offset

1,2

Comments

Denominator of x(n) = A111930(n);

x(n) = a(n)/A111930(n) does not converge.

References

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

Links

Robert Israel, Table of n, a(n) for n = 1..2296

Eric Weisstein's World of Mathematics, Odd Part

Maple

map(numer, ListTools:-PartialSums([seq(1/k/2^padic:-ordp(k, 2), k=1..100)])); # Robert Israel, Dec 28 2017

Mathematica

od[k_] := k/2^IntegerExponent[k, 2];
a[n_] := Sum[od[k]/k^2, {k, 1, n}] // Numerator;
Array[a, 25] (* Jean-François Alcover, Mar 08 2019 *)

Crossrefs

Cf. A000265, A111918, A111920, A111922, A111930.

Sequence in context: A163609 A149779 A125657 * A146030 A098041 A346817

Adjacent sequences: A111926 A111927 A111928 * A111930 A111931 A111932

Keyword

nonn,frac

Author

Reinhard Zumkeller, Aug 21 2005

Status

approved