A246749 Decimal expansion of F'(rho), an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number, where the function F and the constant rho are defined in A246746.

5, 6, 9, 7, 7, 5, 8, 9, 3, 4, 2, 3, 0, 1, 9, 2, 6, 7, 5, 7, 5, 2, 9, 1, 3, 7, 0, 4, 6, 8, 5, 2, 4, 7, 8, 9, 7, 8, 5, 8, 1, 0, 1, 9, 8, 2, 1, 7, 8, 3, 5, 7, 3, 5, 9, 3, 4, 5, 9, 5, 6, 7, 1, 7, 5, 8, 4, 1, 1, 4, 4, 0, 5, 3, 8, 6, 6, 0, 6, 7, 7, 6, 8, 3, 1, 7, 8, 4, 7, 5, 1, 5, 7, 4, 3, 8, 9, 2, 8, 8, 5

Offset

1,1

Links

Table of n, a(n) for n=1..101.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 16.

Kevin Ford, The distribution of Totients

Formula

Let F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.

F'(rho), where rho is the unique solution on [0,1) of F(rho)=1,

Example

5.6977589342301926757529137046852478978581019821783573593459567...

Mathematica

digits = 101; F[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*x^k, {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; F'[x_?NumericQ] := NSum[((k + 1)*Log[k + 1] - k*Log[k] - 1)*k*x^(k - 1), {k, 1, Infinity}, WorkingPrecision -> digits + 10, NSumTerms -> 1000]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[F'[rho], 10, digits] // First

Crossrefs

Cf. A246746.

Sequence in context: A197283 A244843 A118261 * A357471 A021641 A332327

Adjacent sequences: A246746 A246747 A246748 * A246750 A246751 A246752

Keyword

nonn,cons

Author

Jean-François Alcover, Sep 02 2014

Status

approved