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A246751 Decimal expansion of D, an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number. 1
2, 1, 7, 6, 9, 6, 8, 7, 4, 3, 5, 5, 9, 4, 1, 0, 3, 2, 1, 7, 3, 9, 7, 2, 7, 2, 9, 8, 7, 3, 5, 8, 1, 4, 3, 2, 9, 7, 6, 7, 2, 7, 3, 7, 5, 8, 9, 6, 5, 8, 4, 4, 9, 6, 0, 2, 3, 8, 6, 2, 8, 0, 0, 0, 6, 4, 7, 3, 5, 2, 5, 6, 2, 2, 0, 3, 3, 7, 4, 9, 0, 9, 8, 4, 0, 5, 1, 2, 2, 7, 4, 0, 8, 6, 0, 7, 4, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..99.

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.

C = 1/(2*|log(rho)|), where rho is the unique solution on [0,1) of F(rho)=1.

D = 2*C*(1 + log(F'(rho)) - log(2*C)) - 3/2.

EXAMPLE

2.176968743559410321739727298735814329767273758965844960238628...

MATHEMATICA

digits = 99; 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]; c = -1/(2*Log[rho]); d = 2*c*(1 + Log[F'[rho]] - Log[2*c]) - 3/2; RealDigits[d, 10, digits] // First

CROSSREFS

Cf. A246746, A246749, A234614.

Sequence in context: A178049 A257577 A060583 * A295850 A078104 A072280

Adjacent sequences:  A246748 A246749 A246750 * A246752 A246753 A246754

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 02 2014

STATUS

approved

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Last modified April 15 12:55 EDT 2021. Contains 342977 sequences. (Running on oeis4.)