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

1, 4, 12, 48, 240, 240, 1680, 6720, 20160, 4032, 44352, 44352, 576576, 576576, 2882880, 11531520, 196035840, 196035840, 3724680960, 3724680960, 3724680960, 3724680960, 85667662080, 85667662080, 428338310400, 428338310400

Offset: 1

Author

Reinhard Zumkeller, Aug 21 2005

Keywords

• nonn
• frac

Comments

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

x(n) = A111929(n)/a(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

Crossrefs

Cf. A000265, A111919, A111921, A111923.

Programs

Maple

map(denom, 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}] // Denominator;
Array[a, 25] (* Jean-François Alcover, Mar 08 2019 *)