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A344786
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Decimal expansion of (1/e) * Product_{p prime} (1 - 1/p)^(1/p).
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0
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2, 0, 5, 9, 6, 3, 0, 5, 0, 2, 8, 8, 1, 8, 6, 3, 5, 3, 8, 7, 9, 6, 7, 5, 4, 2, 8, 2, 3, 2, 4, 9, 7, 4, 6, 6, 4, 8, 5, 8, 7, 8, 0, 5, 9, 3, 4, 2, 0, 5, 8, 5, 1, 5, 0, 1, 6, 4, 2, 7, 8, 8, 1, 5, 1, 3, 6, 5, 7, 4, 9, 3, 0, 9, 9, 4, 3, 5, 4, 7, 6, 6, 3, 8, 1, 2, 4
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OFFSET
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0,1
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COMMENTS
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Deshouillers and Iwaniec (2008) proved that the sequence of geometric mean values of the Euler totient function, A001088(n)^(1/n) = (Product_{k=1..n} phi(k))^(1/n), is uniformly distributed modulo 1 if and only if this constant is irrational. They noted that Richard Bumby showed that if it is rational, then its denominator has at least 20 decimal digits.
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LINKS
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FORMULA
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Equals exp(-1 - Sum_{k>=2} P(k)/(k-1)), where P(s) is the prime zeta function.
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EXAMPLE
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0.20596305028818635387967542823249746648587805934205...
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MATHEMATICA
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$MaxExtraPrecision = 1000; m = 100; RealDigits[N[Exp[-1 - Sum[PrimeZetaP[k]/(k - 1), {k, 2, 1000}]], m + 1], 10, m][[1]]
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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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