cp's OEIS Frontend

A276184 Numbers n such that A276183(n) = 1.

%I A276184 #19 Nov 05 2016 08:03:12
%S A276184 22,28,30,33,34,37,38,40,43,44,45,48,51,53,54,55,56,61,63,64,65,75,79,
%T A276184 81,83,89,95,101,119,131
%N A276184 Numbers n such that A276183(n) = 1.
%H A276184 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.
%o A276184 (PARI)
%o A276184 A000003(n) = qfbclassno(-4*n);
%o A276184 A000089(n) = {
%o A276184   if (n%4 == 0 || n%4 == 3, return(0));
%o A276184   if (n%2 == 0, n \= 2);
%o A276184   my(f = factor(n), fsz = matsize(f)[1]);
%o A276184   prod(k = 1, fsz, if (f[k, 1] % 4 == 3, 0, 2));
%o A276184 };
%o A276184 A000086(n) = {
%o A276184   if (n%9 == 0 || n%3 == 2, return(0));
%o A276184   if (n%3 == 0, n \= 3);
%o A276184   my(f = factor(n), fsz = matsize(f)[1]);
%o A276184   prod(k = 1, fsz, if (f[k, 1] % 3 == 2, 0, 2));
%o A276184 };
%o A276184 A001615(n) = {
%o A276184   my(f = factor(n), fsz = matsize(f)[1],
%o A276184      g = prod(k=1, fsz, (f[k, 1]+1)),
%o A276184      h = prod(k=1, fsz, f[k, 1]));
%o A276184   return((n*g)\h);
%o A276184 };
%o A276184 A001616(n) = {
%o A276184   my(f = factor(n), fsz = matsize(f)[1]);
%o A276184   prod(k = 1, fsz, f[k, 1]^(f[k, 2]\2) + f[k, 1]^((f[k, 2]-1)\2));
%o A276184 };
%o A276184 A001617(n) = 1 + A001615(n)/12 - A000089(n)/4 - A000086(n)/3 - A001616(n)/2;
%o A276184 A276183(n) = {
%o A276184   my(r = if (n%8 == 3, 4, n%8 == 7, 6, 3));
%o A276184   if (n < 5, 0, (1 + A001617(n))/2 -  r * A000003(n)/12);
%o A276184 };
%o A276184 Vec(select(x->x==1, vector(5000, n, A276183(n)), 1))
%Y A276184 Cf. A276183.
%K A276184 nonn,fini,full
%O A276184 1,1
%A A276184 _Gheorghe Coserea_, Oct 22 2016