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A305756 Coefficients of (q*(j(q)-720))^(1/24) where j(q) is the elliptic modular invariant. 5
1, 1, 8192, 707073, -754075135, -132208502783, 90102565204481, 25124693308972545, -11606164284986636798, -4751761734938773786110, 1495856955988144882193922, 890018844816101689979518466, -181104153998957724140261556733 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

(Conjecture)

Let |b| = 2^p * 3^q * 5^r * ... .

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)

Coefficients of (q*(j(q)+b))^(1/f(b)) are integers.

Especially, coefficients of (q*(j(q)+144*k))^(1/24) are integers.

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)

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..378

CROSSREFS

(q*(j(q)+144*k))^(1/24): A106205 (k=0), this sequence (k=-5), A106203 (k=-12).

(q*(j(q)-720))^(m/24): A305760 (m=-24), A305758 (m=-1), this sequence (m=1).

Cf. A000521, A007240 (j(q)-720), A304020, A305757, A305762.

Sequence in context: A035908 A069274 A220585 * A195661 A017690 A010801

Adjacent sequences:  A305753 A305754 A305755 * A305757 A305758 A305759

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jun 10 2018

STATUS

approved

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Last modified May 6 17:27 EDT 2021. Contains 343586 sequences. (Running on oeis4.)