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A114363 Denominator of zeta(4n)/zeta(2n)^2. 5
1, 5, 7, 715, 7293, 524875, 3547206349, 3393195750, 15419113345821, 26315472459271727875, 261083216622451556697, 2530298441183206558150, 39265828264113994596230058165, 61628134000978439089402342590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

zeta(4n)/zeta(2n)^2 is a rational value expressible in term of Bernoulli's numbers (A027641).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..158

Leo Depuydt, The Prime Sequence: Demonstrably Highly Organized While Also Opaque and Incomputable-With Remarks on Riemann's Hypothesis, Partition, Goldbach's Conjecture, ..., Advances in Pure Mathematics, 4 (No. 8, 2014), 400-466.

FORMULA

Prod( (p^{2n}-1)/(p^{2n}+1) ) = zeta(4n)/zeta(2n)^2 where the product is over all the primes.

MATHEMATICA

a[ n_] := If[ n < 0, 0, Denominator[ Zeta[4*n] / Zeta[2*n]^2 ]] (* Michael Somos, Jan 27 2012 *)

PROG

(PARI) z(n)=bernfrac(2*n)*(-1)^(n - 1)*2^(2*n-1)/(2*n)!;

a(n)=if(n<1, 1, denominator(z(2*n)/z(n)^2))

CROSSREFS

Cf. A027641, A114362.

Sequence in context: A260827 A020467 A089344 * A083687 A101829 A056252

Adjacent sequences:  A114360 A114361 A114362 * A114364 A114365 A114366

KEYWORD

frac,nonn

AUTHOR

Benoit Cloitre, Feb 09 2006; corrected Feb 22 2006

STATUS

approved

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Last modified March 29 05:39 EDT 2020. Contains 333105 sequences. (Running on oeis4.)