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A082020
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Decimal expansion of 15/Pi^2.
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34
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1, 5, 1, 9, 8, 1, 7, 7, 5, 4, 6, 3, 5, 0, 6, 6, 5, 7, 1, 6, 5, 8, 1, 9, 1, 9, 4, 8, 1, 4, 5, 9, 1, 4, 5, 8, 3, 5, 6, 5, 3, 8, 1, 6, 2, 0, 0, 8, 3, 6, 9, 8, 2, 3, 2, 6, 8, 4, 1, 3, 5, 4, 7, 8, 4, 1, 2, 5, 9, 6, 8, 1, 4, 4, 3, 3, 5, 3, 1, 6, 1, 7, 8, 6, 8, 1, 3, 9, 1, 0, 8, 8, 8, 4, 3, 2, 7, 5, 6
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OFFSET
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1,2
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COMMENTS
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3/(2*Pi^2) (the same decimal expansion with an offset 0) is the probability that the greatest common divisor of two numbers selected at random is 2 (Christopher, 1956). - Amiram Eldar, May 23 2020
Equals the asymptotic mean of the abundancy index of the cubefree numbers (A004709) (Jakimczuk and Lalín, 2022). - Amiram Eldar, May 12 2023
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LINKS
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Eric Weisstein's World of Mathematics, Prime Sums.
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FORMULA
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Product_{n >= 1} (1+1/prime(n)^2) = 15/Pi^2 (Ramanujan).
Equals lim_{n->oo} (1/n) * Sum_{k=1..n} psi(k)/k, where psi(k) is the Dedekind psi function (A001615). - Amiram Eldar, May 12 2019.
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EXAMPLE
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1.51981775463506657...
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MAPLE
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MATHEMATICA
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PROG
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(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 15/Pi(R)^2; // G. C. Greubel, Oct 18 2019
(Sage) numerical_approx(15/pi^2, digits=100) # G. C. Greubel, Oct 18 2019
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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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