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A246746 Decimal expansion of 'rho', an auxiliary constant associated with the asymptotic number of values of the Euler totient function less than a given number. 5
5, 4, 2, 5, 9, 8, 5, 8, 6, 0, 9, 8, 4, 7, 1, 0, 2, 1, 9, 5, 9, 3, 8, 4, 5, 9, 5, 7, 7, 9, 4, 6, 9, 4, 2, 6, 7, 7, 9, 5, 0, 4, 6, 1, 6, 1, 9, 5, 3, 9, 2, 4, 6, 9, 6, 6, 5, 1, 5, 7, 8, 1, 0, 3, 4, 7, 0, 8, 9, 3, 1, 8, 9, 4, 7, 6, 4, 5, 6, 2, 2, 3, 2, 9, 5, 9, 3, 7, 4, 7, 4, 5, 1, 3, 4, 8, 9, 1, 0, 9, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..100.

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

Steven R. Finch, Errata and Addenda to Mathematical Constants, January 22, 2016. [Cached copy, with permission of the author]

Kevin Ford, The distribution of Totients

FORMULA

Rho is the unique solution on [0,1) of the equation F(rho)=1, where F(x) = sum_{k >= 1} ((k+1)*log(k+1) - k*log(k) - 1)*x^k.

EXAMPLE

0.54259858609847102195938459577946942677950461619539246966515781...

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]; rho = x /. FindRoot[F[x] == 1, {x, 5/10, 6/10}, WorkingPrecision -> digits + 10]; RealDigits[rho, 10, digits] // First

CROSSREFS

Sequence in context: A213205 A094778 A260849 * A180131 A257972 A222307

Adjacent sequences:  A246743 A246744 A246745 * A246747 A246748 A246749

KEYWORD

nonn,cons

AUTHOR

Jean-Fran├žois Alcover, Sep 02 2014

STATUS

approved

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Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)