A111919 Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^3)).

1, 8, 72, 576, 14400, 1600, 78400, 627200, 50803200, 50803200, 6147187200, 6147187200, 1038874636800, 1038874636800, 1038874636800, 8310997094400, 2401878160281600, 266875351142400, 96342001762406400, 96342001762406400

Offset

1,2

Comments

Numerator of x(n) = A111918(n);

x(n) = A111918(n)/a(n) ---> Pi*Pi/7 = 6*zeta(2)/7.

References

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

Links

Robert Israel, Table of n, a(n) for n = 1..1150

Eric Weisstein's World of Mathematics, Odd Part

Eric Weisstein's World of Mathematics, Riemann Zeta Function zeta(2)

Maple

S:= 0: Res:= NULL:
for k from 1 to 25 do
  S:= S + 1/k^2/2^padic:-ordp(k, 2);
  Res:= Res, denom(S);
od:
Res; # Robert Israel, Jan 13 2020

Mathematica

oddPart[n_] := n/2^IntegerExponent[n, 2];
x[n_] := Sum[oddPart[k]/k^3, {k, 1, n}];
a[n_] := Denominator[x[n]];
Array[a, 20] (* Jean-François Alcover, Dec 13 2021 *)

Prog

(Magma) val:=func<n|n/2^Valuation(n, 2)>; [Denominator(&+[val(k)/(k^3):k in [1..n]]):n in [1..20]]; // Marius A. Burtea, Jan 13 2020

Crossrefs

Cf. A000265, A013661, A111918, A111930, A111921, A111923.

Sequence in context: A270241 A054615 A344067 * A052379 A246940 A158798

Adjacent sequences: A111916 A111917 A111918 * A111920 A111921 A111922

Keyword

nonn,frac

Author

Reinhard Zumkeller, Aug 21 2005

Status

approved