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%I #26 Jun 11 2018 16:56:46
%S 1,1,8192,707073,-754075135,-132208502783,90102565204481,
%T 25124693308972545,-11606164284986636798,-4751761734938773786110,
%U 1495856955988144882193922,890018844816101689979518466,-181104153998957724140261556733
%N Coefficients of (q*(j(q)-720))^(1/24) where j(q) is the elliptic modular invariant.
%C (Conjecture)
%C Let |b| = 2^p * 3^q * 5^r * ... .
%C And f(0) = 24, f(b) = 2^(max(0, min(3, p - 1))) * 3^(max(0, min(1, q - 1))) for |b|>0. (See A305762)
%C Coefficients of (q*(j(q)+b))^(1/f(b)) are integers.
%C Especially, coefficients of (q*(j(q)+144*k))^(1/24) are integers.
%C In case of b = -744, |b| = 2^3 * 3^1 * 31 and f(b) = 4. So coefficients of (q*(j(q)-744))^(1/4) are integers. (See A304020)
%H Seiichi Manyama, <a href="/A305756/b305756.txt">Table of n, a(n) for n = 0..378</a>
%Y (q*(j(q)+144*k))^(1/24): A106205 (k=0), this sequence (k=-5), A106203 (k=-12).
%Y (q*(j(q)-720))^(m/24): A305760 (m=-24), A305758 (m=-1), this sequence (m=1).
%Y Cf. A000521, A007240 (j(q)-720), A304020, A305757, A305762.
%K sign
%O 0,3
%A _Seiichi Manyama_, Jun 10 2018
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