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%I #24 Jan 03 2021 17:30:25
%S 0,3,7,2,7,6,8,1,0,2,9,6,4,5,1,6,5,8,1,5,0,9,8,0,7,8,5,6,5,1,6,4,4,6,
%T 1,8,0,3,6,2,8,2,3,7,9,4,8,2,7,8,3,0,0,6,7,0,4,1,0,2,2,1,3,4,7,7,5,1,
%U 3,9,2,9,1,0,2,0,3,6,7,5,5,3,2,3,0,0,3,4,3,1,4,7,0,6,5,8,2,9,8,9,0
%N Decimal expansion of q between 0 and 1 maximizing Dedekind eta function eta(q) = q^(1/24) * Product_{n>=1} (1 - q^n).
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/DedekindEtaFunction.html">Dedekind Eta Function</a>
%F Root of the equation Sum_{k>=1} A000203(k) * r^k = 1/24. - _Vaclav Kotesovec_, Jun 28 2017
%F Equals A057823^2. - _Vaclav Kotesovec_, Jul 02 2017
%e 0.0372768102964516581509807856516446180362823794827830067...
%t q /. Last @ FindMaximum[ DedekindEta[ -I*Log[q]/(2*Pi)], {q, 1/25}, WorkingPrecision -> 200] // RealDigits[#][[1]][[1 ;; 100]]& // Prepend[#, 0]&
%t x /. FindRoot[24*Sum[DivisorSigma[1, k]*x^k, {k, 1, 1000}] == 1, {x, 1}, WorkingPrecision -> 101] (* _Vaclav Kotesovec_, Jun 28 2017 *)
%Y Cf. A000203, A057823, A288877, A289392.
%K nonn,cons
%O 0,2
%A _Jean-François Alcover_, Feb 05 2013
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