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A198775 Numbers having exactly four representations by the quadratic form x^2+xy+y^2 with 0<=x<=y. 8

%I

%S 1729,2821,3367,3913,4123,4459,4921,5187,5551,5719,6097,6517,6643,

%T 6916,7189,7657,8029,8113,8463,8827,8911,9139,9331,9373,9709,9919,

%U 10101,10507,10621,10633,11137,11284,11557,11739,12369,12649,12691,12901,13237,13377

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

%C A088534(a(n)) = 4; subsequence of A118886, see also A003136.

%H Reinhard Zumkeller, <a href="/A198775/b198775.txt">Table of n, a(n) for n = 1..250</a>

%e a(1) = 1729 = 3^2+3*40+40^2 = 8^2+8*37+37^2 = 15^2+15*32+32^2 = 23^2+23*25+25^2, A088534(1729) = 4;

%e a(10) = 5719 = 5^2+5*73+73^2 = 15^2+15*67+67^2 = 18^2+18*65+65^2 = 37^2+37*50+50^2, A088534(5719) = 4;

%e a(100) = 23779 = 17^2+17*145+145^2 = 30^2+30*137+137^2 = 50^2+50*123+123^2 = 85^2+85*93+93^2, A088534(23779) = 4.

%t amax = 20000; 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 A198775 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 4&] (* _Jean-Fran├žois Alcover_, Jun 21 2018 *)

%o (Haskell)

%o a198775 n = a198775_list !! (n-1)

%o a198775_list = filter ((== 4) . a088534) a003136_list

%Y Cf. A198772, A198773, A198774.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Oct 30 2011

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Last modified September 17 19:15 EDT 2019. Contains 327137 sequences. (Running on oeis4.)