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A065485
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Decimal expansion of Murata's constant Product_{p prime}(1 + 1/(p-1)^2).
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9
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2, 8, 2, 6, 4, 1, 9, 9, 9, 7, 0, 6, 7, 5, 9, 1, 5, 7, 5, 5, 4, 6, 3, 9, 1, 7, 4, 7, 2, 3, 6, 9, 5, 3, 7, 4, 9, 0, 1, 3, 0, 4, 1, 1, 0, 5, 4, 5, 9, 2, 6, 6, 8, 7, 6, 1, 7, 9, 7, 4, 5, 8, 3, 4, 5, 3, 0, 7, 5, 7, 6, 2, 4, 4, 5, 9, 7, 6, 2, 4, 0, 5, 5, 3, 3, 4, 5, 8, 6, 6, 4, 9, 8, 8, 1, 8, 4, 4, 5
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals lim_{k->oo} (1/pi(k)) * Sum_{p prime, p <= k} (p-1)/phi(p-1), where pi(k) = A000720(k) and phi(k) = A000010(k) (Murata, 1991). - Amiram Eldar, Jul 31 2020
Equals Sum_{k>=1} mu(k)^2/phi(k)^2, where mu is the Möbius function (A008683) and phi is the Euler totient function (A000010). - Amiram Eldar, Jan 14 2022
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EXAMPLE
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2.8264199970675915755463917472369537490...
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MATHEMATICA
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digits = 99; terms = 1000; $MaxExtraPrecision = 500; r[n_Integer] := 2 - (1-I)^(n+1) - (1+I)^(n+1); NSum[r[n-1]*PrimeZetaP[n]/n, {n, 2, terms}, NSumTerms -> terms, WorkingPrecision -> digits+10] // Exp // RealDigits[ #, 10, digits]& // First (* Jean-François Alcover, Apr 16 2016 *)
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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