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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. 1
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 (list; constant; graph; refs; listen; history; text; internal format)
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 * A021641 A332327 A260635

Adjacent sequences:  A246746 A246747 A246748 * A246750 A246751 A246752

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 02 2014

STATUS

approved

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Last modified October 20 18:43 EDT 2021. Contains 348118 sequences. (Running on oeis4.)