A116569 Ono prime weight function divided by 6.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 4, 10, 10, 20, 10, 20, 35, 20, 35, 56, 56, 56, 84, 84, 120, 84, 120, 165, 220, 220, 220, 286, 286, 286, 364, 455, 455, 560, 455, 680, 560, 680, 680, 816, 969, 1140, 969

Offset

1,13

Links

Table of n, a(n) for n=1..50.

Ken Ono and Scott Ahlgren, Weierstrass points on X0(p) and supersingular j-invariants, Mathematische Annalen 325, 2003, pp. 355-368.

Mathematica

g[1] = 1; g[2] = 1;
g[n_] := (Prime[n] - 13)/12 /; Mod[Prime[n], 12] - 1 == 0;
g[n_] := (Prime[n] - 5)/12 /; Mod[Prime[n], 12] - 5 == 0;
g[n_] := (Prime[n] - 7)/12 /; Mod[Prime[n], 12] - 7 == 0;
g[n_] := (Prime[n] + 1)/12 /; Mod[Prime[n], 12] - 11 == 0;
Table[g[n]*(g[n]^2 - 1)/6, {n, 1, 50}]

Prog

(PARI) a(n) = {if (n < 3, g = 1, p = prime(n); m = p % 12; g = if (m==1, (p-13)/12, if (m==5, (p-5)/12, if (m==7, (p-7)/12, if (m==11, (p+1)/12))))); g*(g^2-1)/6; } \\ Michel Marcus, Apr 06 2018

Crossrefs

Cf. A116563.

Sequence in context: A167132 A168326 A101256 * A058187 A188271 A219939

Adjacent sequences: A116566 A116567 A116568 * A116570 A116571 A116572

Keyword

nonn,uned,obsc

Author

Roger L. Bagula, Mar 18 2006

Extensions

Offset corrected by Michel Marcus, Apr 06 2018

Status

approved