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A054730 Odd n such that genus of modular curve X_0(N) is never equal to n.

%I A054730 #18 May 25 2016 11:49:43
%S A054730 49267,74135,94091,96463,102727,107643,118639,138483,145125,181703,
%T A054730 182675,208523,221943,237387,240735,245263,255783,267765,269627,
%U A054730 272583,277943,280647,283887,286815,309663,313447,322435,326355,336675,347823,352719
%N A054730 Odd n such that genus of modular curve X_0(N) is never equal to n.
%C A054730 There are 4329 odd integers in the sequence less than 10^7. - _Gheorghe Coserea_, May 23 2016
%D A054730 J. A. Csirik, The genus of X_0(N) is not 150, preprint, 2000.
%H A054730 Gheorghe Coserea, <a href="/A054730/b054730.txt">Table of n, a(n) for n = 1..4329</a>
%H A054730 J. A. Csirik, M. Zieve, and J. Wetherell, <a href="http://arXiv.org/abs/math/0006096">On the genera of X0(N)</a>, arXiv:math/0006096 [math.NT], 2000.
%o A054730 (PARI)
%o A054730 A000089(n) = {
%o A054730   if (n%4 == 0 || n%4 == 3, return(0));
%o A054730   if (n%2 == 0, n \= 2);
%o A054730   my(f = factor(n), fsz = matsize(f)[1]);
%o A054730   prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2));
%o A054730 };
%o A054730 A000086(n) = {
%o A054730   if (n%9 == 0 || n%3 == 2, return(0));
%o A054730   if (n%3 == 0, n \= 3);
%o A054730   my(f = factor(n), fsz = matsize(f)[1]);
%o A054730   prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2));
%o A054730 };
%o A054730 A001615(n) = {
%o A054730   my(f = factor(n), fsz = matsize(f)[1],
%o A054730      g = prod(k=1, fsz, (f[k, 1]+1)),
%o A054730      h = prod(k=1, fsz, f[k, 1]));
%o A054730   return((n*g)\h);
%o A054730 };
%o A054730 A001616(n) = {
%o A054730   my(f = factor(n), fsz = matsize(f)[1]);
%o A054730   prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2));
%o A054730 };
%o A054730 A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2;
%o A054730 scan(n) = {
%o A054730   my(inv = vector(n+1, g, -1), bnd = 12*n + 18*sqrtint(n) + 100, g);
%o A054730   for (k = 1, bnd, g = A001617(k);
%o A054730        if (g <= n && inv[g+1] == -1, inv[g+1] = k));
%o A054730   select(x->(x%2==1), apply(x->(x-1), Vec(select(x->x==-1, inv, 1))));
%o A054730 };
%o A054730 scan(400*1000)
%Y A054730 Cf. A054726, A054727, A054729.
%K A054730 nonn
%O A054730 1,1
%A A054730 Janos A. Csirik, Apr 21 2000
%E A054730 More terms from _Gheorghe Coserea_, May 23 2016
%E A054730 Offset corrected by _Gheorghe Coserea_, May 23 2016