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A114363
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Denominator of zeta(4n)/zeta(2n)^2.
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9
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1, 5, 7, 715, 7293, 524875, 3547206349, 3393195750, 15419113345821, 26315472459271727875, 261083216622451556697, 2530298441183206558150, 39265828264113994596230058165, 61628134000978439089402342590
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OFFSET
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0,2
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COMMENTS
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zeta(4n)/zeta(2n)^2 is a rational value expressible in term of Bernoulli's numbers (A027641).
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LINKS
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FORMULA
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Product_{p primes} (p^{2n}-1)/(p^{2n}+1) ) = zeta(4n)/zeta(2n)^2.
For n > 0, a(n) = Denominator((D(n) - N(n)) / (D(n) + N(n))), where N(n) = A348829(n) and D(n) = A348830(n). See my comments and formulas in A348829. - Thomas Ordowski, Feb 12 2022
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EXAMPLE
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2/1, 2/5, 6/7, 691/715, 7234/7293, 523833/524875, 3545461365/3547206349, ...
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MATHEMATICA
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a[ n_] := If[ n < 0, 0, Denominator[ Zeta[4*n] / Zeta[2*n]^2 ]] (* Michael Somos, Jan 27 2012 *)
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PROG
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(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))
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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