cp's OEIS Frontend

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.

%I A246746 #19 Jan 17 2020 16:03:42
%S A246746 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,
%T A246746 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,
%U A246746 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
%N 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.
%H A246746 Steven R. Finch, <a href="http://arxiv.org/abs/2001.00578">Errata and Addenda to Mathematical Constants</a>, p. 16.
%H A246746 Kevin Ford, <a href="http://www.math.uiuc.edu/~ford/wwwpapers/totients.pdf">The distribution of Totients</a>
%F A246746 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.
%e A246746 0.54259858609847102195938459577946942677950461619539246966515781...
%t A246746 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
%K A246746 nonn,cons
%O A246746 0,1
%A A246746 _Jean-François Alcover_, Sep 02 2014