A305758 -id:A305758 - cp's OEIS frontend

A305756 Coefficients of (q*(j(q)-720))^(1/24) where j(q) is the elliptic modular invariant.

1, 1, 8192, 707073, -754075135, -132208502783, 90102565204481, 25124693308972545, -11606164284986636798, -4751761734938773786110, 1495856955988144882193922, 890018844816101689979518466, -181104153998957724140261556733

Offset: 0

Seiichi Manyama, Jun 10 2018

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(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)

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

(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.

A305760 Coefficients of 1/(q*(j(q)-720)) where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, -24, -196308, -12057152, 38590826190, 5667574866912, -7304962792606024, -1755598494902269440, 1325502689549152990437, 465173370338426065214640, -228213884020015849568089308, -112934890287321570650976240384

Offset: 0

Seiichi Manyama, Jun 10 2018

sign

Seiichi Manyama, Table of n, a(n) for n = 0..376

(q*(j(q)-720))^(m/24): this sequence (m=-24), A305758 (m=-1), A305756 (m=1).

Cf. A000521, A007240 (j(q)-720), A305699, A305757.

G.f.: Product_{k>0} (1 - x^k)^A305757(k).

cp's OEIS Frontend

A305756 Coefficients of (q*(j(q)-720))^(1/24) where j(q) is the elliptic modular invariant.

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