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Numbers having exactly three representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.
8

%I #11 Jun 21 2018 10:32:37

%S 637,931,1183,1519,1813,1911,2107,2401,2527,2548,2793,2989,3211,3283,

%T 3549,3577,3724,3871,4557,4693,4732,4753,5047,5239,5341,5439,5733,

%U 6076,6223,6253,6321,6727,6811,7203,7252,7267,7399,7581,7644,7693,7987,8379,8428

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

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

%H Reinhard Zumkeller, <a href="/A198774/b198774.txt">Table of n, a(n) for n = 1..1000</a>

%e a(1) = 637 = 4^2+4*23+23^2 = 7^2+7*21+21^2 = 12^2+12*17+17^2, A088534(637)=3;

%e a(2) = 931 = 1^2+1*30+30^2 = 9^2+9*25+25^2 = 14^2+14*21+21^2, A088534(273)=3.

%t 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}];

%t A198774 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 3&] (* _Jean-François Alcover_, Jun 21 2018 *)

%o (Haskell)

%o a198774 n = a198774_list !! (n-1)

%o a198774_list = filter ((== 3) . a088534) a003136_list

%Y Cf. A198772, A198773, A198775.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Oct 30 2011