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%I #34 Oct 24 2016 15:47:41
%S 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,23,24,25,26,27,
%T 29,31,32,35,36,39,41,47,49,50,59,71
%N Fricke's 37 cases for two-valued modular equations.
%H Harvey Cohn, <a href="https://doi.org/10.1090/S0025-5718-1988-0935079-4">Fricke's Two-Valued Modular Equations</a>, Math. Comp. 51 (1988), 787-807.
%F Numbers n>1 such that 0 = A276183(n).
%o (PARI)
%o A000003(n) = qfbclassno(-4*n);
%o A000089(n) = {
%o if (n%4 == 0 || n%4 == 3, return(0));
%o if (n%2 == 0, n \= 2);
%o my(f = factor(n), fsz = matsize(f)[1]);
%o prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2));
%o };
%o A000086(n) = {
%o if (n%9 == 0 || n%3 == 2, return(0));
%o if (n%3 == 0, n \= 3);
%o my(f = factor(n), fsz = matsize(f)[1]);
%o prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2));
%o };
%o A001615(n) = {
%o my(f = factor(n), fsz = matsize(f)[1],
%o g = prod(k=1, fsz, (f[k, 1]+1)),
%o h = prod(k=1, fsz, f[k, 1]));
%o return((n*g)\h);
%o };
%o A001616(n) = {
%o my(f = factor(n), fsz = matsize(f)[1]);
%o prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2));
%o };
%o A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2;
%o A276183(n) = {
%o my(r = if (n%8 == 3, 4, n%8 == 7, 6, 3));
%o if (n < 5, 0, (1 + A001617(n))/2 - r * A000003(n)/12);
%o };
%o select(x->(x>1), Vec(select(x->x==0, vector(100, n, A276183(n)), 1)))
%Y Cf. A000003, A001617.
%K nonn,fini,full
%O 1,1
%A _Gheorghe Coserea_, Oct 17 2016
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