A198774 Numbers having exactly three representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.

637, 931, 1183, 1519, 1813, 1911, 2107, 2401, 2527, 2548, 2793, 2989, 3211, 3283, 3549, 3577, 3724, 3871, 4557, 4693, 4732, 4753, 5047, 5239, 5341, 5439, 5733, 6076, 6223, 6253, 6321, 6727, 6811, 7203, 7252, 7267, 7399, 7581, 7644, 7693, 7987, 8379, 8428

Offset: 1

Author

Reinhard Zumkeller, Oct 30 2011

Keywords

• nonn

Comments

A088534(a(n)) = 3; subsequence of A118886, see also A003136.

Examples

			a(1) = 637 = 4^2+4*23+23^2 = 7^2+7*21+21^2 = 12^2+12*17+17^2, A088534(637)=3;
a(2) = 931 = 1^2+1*30+30^2 = 9^2+9*25+25^2 = 14^2+14*21+21^2, A088534(273)=3.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A198772, A198773, A198775.

Programs

Haskell

a198774 n = a198774_list !! (n-1)
a198774_list = filter ((== 3) . a088534) a003136_list

Mathematica

amax = 10000; xmax = Sqrt[amax] // Ceiling; Clear[f]; f[_] = 0; Do[q = x^2 + x y + y^2; f[q] = f[q] + 1, {x, 0, xmax}, {y, x, xmax}];
A198774 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 3&] (* Jean-François Alcover, Jun 21 2018 *)