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 A054730 Odd n such that genus of modular curve X_0(N) is never equal to n. 2
 49267, 74135, 94091, 96463, 102727, 107643, 118639, 138483, 145125, 181703, 182675, 208523, 221943, 237387, 240735, 245263, 255783, 267765, 269627, 272583, 277943, 280647, 283887, 286815, 309663, 313447, 322435, 326355, 336675, 347823, 352719 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are 4329 odd integers in the sequence less than 10^7. - Gheorghe Coserea, May 23 2016 REFERENCES J. A. Csirik, The genus of X_0(N) is not 150, preprint, 2000. LINKS Gheorghe Coserea, Table of n, a(n) for n = 1..4329 J. A. Csirik, M. Zieve, and J. Wetherell, On the genera of X0(N), arXiv:math/0006096 [math.NT], 2000. PROG (PARI) A000089(n) = {   if (n%4 == 0 || n%4 == 3, return(0));   if (n%2 == 0, n \= 2);   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2)); }; A000086(n) = {   if (n%9 == 0 || n%3 == 2, return(0));   if (n%3 == 0, n \= 3);   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2)); }; A001615(n) = {   my(f = factor(n), fsz = matsize(f)[1],      g = prod(k=1, fsz, (f[k, 1]+1)),      h = prod(k=1, fsz, f[k, 1]));   return((n*g)\h); }; A001616(n) = {   my(f = factor(n), fsz = matsize(f)[1]);   prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2)); }; A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2; scan(n) = {   my(inv = vector(n+1, g, -1), bnd = 12*n + 18*sqrtint(n) + 100, g);   for (k = 1, bnd, g = A001617(k);        if (g <= n && inv[g+1] == -1, inv[g+1] = k));   select(x->(x%2==1), apply(x->(x-1), Vec(select(x->x==-1, inv, 1)))); }; scan(400*1000) CROSSREFS Cf. A054726, A054727, A054729. Sequence in context: A305696 A184663 A184660 * A253379 A253372 A204227 Adjacent sequences:  A054727 A054728 A054729 * A054731 A054732 A054733 KEYWORD nonn AUTHOR Janos A. Csirik, Apr 21 2000 EXTENSIONS More terms from Gheorghe Coserea, May 23 2016 Offset corrected by Gheorghe Coserea, May 23 2016 STATUS approved

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Last modified August 7 15:08 EDT 2020. Contains 336276 sequences. (Running on oeis4.)