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A191622
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Decimal expansion of the growth constant for the partial sums of maximal unitary squarefree divisors.
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3
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6, 4, 9, 6, 0, 6, 6, 9, 9, 3, 3, 7, 3, 4, 1, 1, 9, 4, 7, 3, 3, 9, 0, 4, 8, 8, 0, 4, 8, 0, 2, 1, 2, 1, 2, 6, 7, 0, 3, 8, 1, 0, 8, 9, 9, 3, 1, 9, 8, 8, 2, 8, 8, 3, 9, 1, 8, 3, 2, 1, 0, 3, 9, 2, 6, 1, 3, 2, 0, 7, 1, 0, 4, 2, 8, 9, 5, 5, 1, 4, 6, 2, 7, 2, 0, 3, 5, 3, 5, 1, 9, 3, 7, 2, 1, 1, 9, 8, 0, 0, 7, 2, 0, 3, 8, 5
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OFFSET
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0,1
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COMMENTS
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The partial sums grow Sum_{n=1..N} A055231(n) = (this constant)*N^2/2 +O(N^(3/2)).
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LINKS
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Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 52 (constant beta).
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FORMULA
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Equals Product_{primes p=2,3,5,7,...} ( 1 - (p^2+p-1)/(p^3*(p+1)) ).
The constant d2 in the paper by Cloutier et al. such that Sum_{k=1..x} 1/A057521(x) = d2*x + O(x^(1/2)). - Amiram Eldar, Oct 01 2019
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EXAMPLE
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0.64960669933734119473390488048021212670381089931988288391832103926132071...
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MATHEMATICA
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$MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{-2, 0, 2, 0, -1}, {0, -2, 0, 2, -5}, m]; RealDigits[Exp[NSum[Indexed[c, n]*PrimeZetaP[n]/n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]] (* Amiram Eldar, Jun 19 2019 *)
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PROG
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(PARI) prodeulerrat(1 - (p^2+p-1)/(p^3*(p+1))) \\ Amiram Eldar, Mar 17 2021
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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