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 A198775 Numbers having exactly four representations by the quadratic form x^2+xy+y^2 with 0<=x<=y. 8
 1729, 2821, 3367, 3913, 4123, 4459, 4921, 5187, 5551, 5719, 6097, 6517, 6643, 6916, 7189, 7657, 8029, 8113, 8463, 8827, 8911, 9139, 9331, 9373, 9709, 9919, 10101, 10507, 10621, 10633, 11137, 11284, 11557, 11739, 12369, 12649, 12691, 12901, 13237, 13377 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A088534(a(n)) = 4; subsequence of A118886, see also A003136. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..250 EXAMPLE 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; 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; 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. MATHEMATICA 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}]; A198775 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 4&] (* Jean-François Alcover, Jun 21 2018 *) PROG (Haskell) a198775 n = a198775_list !! (n-1) a198775_list = filter ((== 4) . a088534) a003136_list CROSSREFS Cf. A198772, A198773, A198774. Sequence in context: A051388 A033181 A300949 * A154729 A083737 A182208 Adjacent sequences:  A198772 A198773 A198774 * A198776 A198777 A198778 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 30 2011 STATUS approved

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Last modified August 19 04:27 EDT 2019. Contains 326109 sequences. (Running on oeis4.)