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

Author

Reinhard Zumkeller, Aug 21 2005

Keywords

• nonn
• frac

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)

Crossrefs

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

Programs

Magma

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

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 *)