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A157296
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Decimal expansion of 31185/(2*Pi^8).
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2
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1, 6, 4, 3, 2, 9, 9, 6, 8, 1, 8, 5, 7, 0, 9, 9, 9, 9, 2, 2, 7, 7, 4, 8, 0, 1, 8, 0, 1, 2, 9, 1, 4, 9, 7, 8, 4, 6, 0, 8, 2, 8, 7, 5, 8, 4, 4, 5, 7, 2, 3, 5, 0, 9, 8, 5, 9, 5, 8, 3, 4, 5, 0, 5, 1, 6, 4, 3, 2, 8, 6, 4, 8, 1, 2, 4, 5, 5, 1, 7, 4, 9, 5, 3, 7, 5, 1, 3, 7, 4, 2, 3, 7, 6, 5, 4, 9, 2, 9, 5, 6, 5, 8, 2, 8
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OFFSET
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1,2
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COMMENTS
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Equals the asymptotic mean of the abundancy index of the 9-free numbers (numbers that are not divisible by a 9th power other than 1) (Jakimczuk and Lalín, 2022). - Amiram Eldar, May 12 2023
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LINKS
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FORMULA
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Equals Product_{p = primes = A000040} (1+1/p^2+1/p^4+1/p^6+1/p^8). The variant Product_{p} (1+1/p^2+1/p^6+1/p^8) equals A082020*Product_{p} (1+1/p^6) = A082020*zeta(6)/zeta(12) = 10135125/(691*Pi^8).
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EXAMPLE
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1.64329968185709999227... = (1+1/2^2+1/2^4+1/2^6+1/2^8)*(1+1/3^2+1/3^4+1/3^6+1/3^8)*(1+1/5^2+1/5^4+1/5^6+1/5^8)*...
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MAPLE
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evalf(31185/2/Pi^8) ;
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MATHEMATICA
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RealDigits[31185/(2*Pi^8), 10, 120][[1]] (* Harvey P. Dale, Mar 30 2018 *)
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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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