%I #18 Apr 12 2018 04:29:21
%S 2,2,4,2,8,4,4,4,8,4,12,4,8,8,8,4,16,4,12,8,16,4,12,8,8,12,12,4,24,8,
%T 12,8,16,8,24,8,8,12,16,8,32,8,12,12,16,8,20,8,16,12,24,8,24,12,16,16,
%U 16,4,36,8,24,16,16,8,32,16,12,16,32,8,28,8,16,20,24,12,32,8,20,16,24,8,36,16,16,20,24,8,48,16,24,12,16,16,32,16,16,16,24,8
%N a(n) is the algebraic order of the elliptic lambda function lambda^*(n), where lambda^*(n) is the value of k_n such that K'(k_n)/K(k_n) = sqrt(n), K(k) is a complete elliptic function and K'(k) is the complementary function.
%H Vaclav Kotesovec, <a href="/A084540/b084540.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EllipticLambdaFunction.html">Elliptic Lambda Function</a>
%e k_3 = 1/4 Sqrt[2](Sqrt[3]-1) = Root[1-16*#1^2+16*#1^4&,3], so a(3) = 4.
%t Table[Exponent[MinimalPolynomial[RootApproximant[N[Sqrt[ModularLambda[I*Sqrt[n]]], 100*n]], x], x], {n, 1, 50}] (* _Vaclav Kotesovec_, Apr 07 2018 *)
%Y Cf. A115977.
%K nonn
%O 1,1
%A _Eric W. Weisstein_, May 29 2003
%E a(29)-a(100) from _Vaclav Kotesovec_, Apr 07 2018