A344786 Decimal expansion of (1/e) * Product_{p prime} (1 - 1/p)^(1/p).

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

Offset

0,1

Comments

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.

Links

Table of n, a(n) for n=0..86.

Jean-Marc Deshouillers and Henryk Iwaniec, On the distribution modulo one of the mean values of some arithmetical functions, Uniform Distribution Theory, Vol. 3, No. 1 (2008), pp. 111-124.

Mehdi Hassani, Uniform distribution modulo one of some sequences concerning the Euler function, Rev. Un. Mat. Argentina, Vol. 54, No. 1 (2013), pp. 55-68.

Formula

Equals exp(-1 - Sum_{k>=2} P(k)/(k-1)), where P(s) is the prime zeta function.

Example

0.20596305028818635387967542823249746648587805934205...

Mathematica

$MaxExtraPrecision = 1000; m = 100; RealDigits[N[Exp[-1 - Sum[PrimeZetaP[k]/(k - 1), {k, 2, 1000}]], m + 1], 10, m][[1]]

Crossrefs

Cf. A000010, A001088, A068985.

Sequence in context: A374063 A243445 A227569 * A011014 A002976 A358305

Adjacent sequences: A344783 A344784 A344785 * A344787 A344788 A344789

Keyword

nonn,cons

Author

Amiram Eldar, May 28 2021

Status

approved