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A116571 Coefficient expansion of wfunction based on prime genus weight function. 0

%I

%S 6,6,6,6,24,24,60,60,120,60,120,210,120,210,336,336,336,504,504,720,

%T 504,720,990,1320,1320,1320,1716,1716,1716,2184,2730,2730,3360,2730,

%U 4080,3360,4080,4080,4896,5814,6840,5814,6840,7980,6840,9240,9240,10626

%N Coefficient expansion of wfunction based on prime genus weight function.

%H Ken Ono and Scott Ahlgren, <a href="https://uva.theopenscholar.com/files/ken-ono/files/070.pdf">Weierstrass points on X0(p) and supersingular j-invariants</a>, Mathematische Annalen 325, 2003, pp. 355-368.

%t g[1] = 1; g[2] = 1;

%t g[n_] := (Prime[n] - 13)/12 /; Mod[Prime[n], 12] - 1 == 0

%t g[n_] := (Prime[n] - 5)/12 /; Mod[Prime[n], 12] - 5 == 0

%t g[n_] := (Prime[n] - 7)/12 /; Mod[Prime[n], 12] - 7 == 0

%t g[n_] := (Prime[n] + 1)/12 /; Mod[Prime[n], 12] - 11 == 0

%t p[x] := Sum[g[n]*(g[n]^2 - 1)*x^n, {n, 1, 200}]

%t Flatten[{{0}, Table[ Coefficient[Series[p[x], {x, 0, 70}], x^n], {n, 1, 70}]}]

%K nonn,obsc,uned

%O 0,1

%A _Roger L. Bagula_, Mar 18 2006

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Last modified September 22 05:11 EDT 2021. Contains 347605 sequences. (Running on oeis4.)