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 A198772 Numbers having exactly one representation by the quadratic form x^2 + xy + y^2 with 0 <= x <= y. 9
 0, 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 25, 27, 28, 31, 36, 37, 39, 43, 48, 52, 57, 61, 63, 64, 67, 73, 75, 76, 79, 81, 84, 93, 97, 100, 103, 108, 109, 111, 112, 117, 121, 124, 127, 129, 139, 144, 148, 151, 156, 157, 163, 171, 172, 175, 181, 183, 189, 192, 193 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA A088534(a(n)) = 1. a(n) = A034022(n) for n <= 32. EXAMPLE a(20) = 48 = 4^2 + 4*4 + 4^2, A088534(48) = 1; a(21) = 52 = 2^2 + 2*6 + 6^2, A088534(52) = 1. MATHEMATICA amax = 200; 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}]; A198772 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 1&] (* Jean-François Alcover, Jun 21 2018 *) PROG (Haskell) a198772 n = a198772_list !! (n-1) a198772_list = filter ((== 1) . a088534) a003136_list (Julia) function isA198772(n)     M = Int(round(2*sqrt(n/3)))     count = 0     for y in 0:M, x in 0:y         n == x^2 + y^2 + x*y && (count += 1)         count == 2 && break     end     return count == 1 end A198772list(upto) = [n for n in 0:upto if isA198772(n)] A198772list(193) |> println # Peter Luschny, Mar 17 2018 CROSSREFS Subsequence of Loeschian numbers A003136. Complement of A118886 with respect to A003136. Cf. A198773, A198774, A198775. Sequence in context: A326421 A329963 A034022 * A185256 A070992 A246514 Adjacent sequences:  A198769 A198770 A198771 * A198773 A198774 A198775 KEYWORD nonn AUTHOR Reinhard Zumkeller, Oct 30 2011 STATUS approved

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Last modified April 19 15:00 EDT 2021. Contains 343116 sequences. (Running on oeis4.)