A068589 Denominator(Sum_{i=1..n} 1/i^3)/denominator(Sum_{i=1..n} 1/i).

1, 4, 36, 144, 3600, 1200, 58800, 235200, 6350400, 6350400, 768398400, 768398400, 129859329600, 129859329600, 129859329600, 519437318400, 150117385017600, 50039128339200, 18064125330451200, 18064125330451200, 54192375991353600

Offset: 1

Author

Benoit Cloitre, Mar 27 2002

Keywords

• easy
• nonn

Comments

For n = 1 to n = 19, we have a(n) = A334580(n), but a(20) = 18064125330451200 <> 3612825066090240 = A334580(20). - Petros Hadjicostas, May 06 2020

Crossrefs

Cf. A002805, A007409, A119682, A334580.

Programs

Maple

a := proc(n) local i: denom(add(1/i^3, i = 1 .. n))/denom(add(1/i, i = 1 .. n)): end proc:
seq(a(n), n=1..30); # Petros Hadjicostas, May 06 2020

PARI

a(n) = denominator(sum(k=1, n, 1/k^3)/sum(k=1, n, 1/k)); \\ Michel Marcus, May 07 2020

Formula

a(n) = A007409(n)/A002805(n).