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#21 by Hugo Pfoertner at Wed Aug 25 13:00:38 EDT 2021
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#20 by Michel Marcus at Wed Aug 25 12:08:17 EDT 2021
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#19 by Michel Marcus at Wed Aug 25 12:08:00 EDT 2021
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| LINKS
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R. J. Mathar, <a href="http://arxiv.org/abs/1008.2547">Table of Dirichlet L-series and Prime Zeta Modulo Functions for Small Moduli</a>, arXiv:1008.2547 [math.NT]], ], 2010-2015.
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| STATUS
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approved
editing
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#18 by N. J. A. Sloane at Mon Jun 07 09:17:07 EDT 2021
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#17 by N. J. A. Sloane at Mon Jun 07 09:16:37 EDT 2021
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| COMMENTS
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This constant can be considered as an equivalentanalog of zeta(3) (= Apéry's constant = A002117), where Euler's zeta(3) is over all positive integers, with prime elements in A000040, while this constant is over all positive integers that can be written as the sum of two squares (A001481) with prime elements given in A055025.
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| STATUS
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proposed
editing
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#16 by A.H.M. Smeets at Mon Jun 07 06:49:49 EDT 2021
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#15 by A.H.M. Smeets at Mon Jun 07 06:49:42 EDT 2021
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| COMMENTS
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This constant can be considered as an equivalent of zeta(3) (= Apéry's constant = A002117), where Euler's zeta(3) is over all positive integers, with prime elements in A000040, while this constant is over all positive integers that can be written as the sum of two squares (A001481) with prime elements given in A055025.
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proposed
editing
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#14 by A.H.M. Smeets at Sun Jun 06 05:40:29 EDT 2021
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#13 by A.H.M. Smeets at Sun Jun 06 05:38:31 EDT 2021
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| NAME
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Decimal expansion of zeta(3) over the numbers that can be written as the sum of two squares, i.e., A001481.
Decimal expansion of Sum_{i > 0} 1/A001481(i)^3.
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| FORMULA
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Equals 1/(1-prime(1)^(-3)) / )) * Product_{i>1 and prime(i) == 1 (mod 4)} ()} 1/(1-prime(i)^(-3)) / )) * Product_{i>1 and prime(i) == 3 (mod 4)} ()} 1/(1-prime(i)^(-6)), where prime(n) = A000040(n).
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#12 by N. J. A. Sloane at Sat Jun 05 17:20:59 EDT 2021
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