%I #37 Jun 21 2018 21:22:22
%S 49,91,133,147,169,196,217,247,259,273,301,343,361,364,399,403,427,
%T 441,469,481,507,511,532,553,559,588,589,637,651,676,679,703,721,741,
%U 763,777,784,793,817,819,868,871,889,903,931,949,961,973,988,1027,1029,1036,1057,1083,1092,1099
%N Numbers expressible as x^2 + x*y + y^2, 0 <= x <= y, in 2 or more ways.
%C Squares of distances between two points in the triangular lattice in two or more nontrivially different ways.
%C Numbers whose prime factorization contains at least two (not necessarily distinct) primes congruent to 1 mod 6 and any prime factor congruent to 2 mod 3 has even multiplicity. Products of two elements of A024606.
%C If k is in the sequence then so is k * m^2 for m > 0. - _David A. Corneth_, Jun 21 2018
%H Reinhard Zumkeller, <a href="/A118886/b118886.txt">Table of n, a(n) for n = 1..10000</a>
%H A. Mazel, I. Stuhl, Y. Suhov, <a href="https://arxiv.org/abs/1803.04041">Hard-core configurations on a triangular lattice and Eisenstein primes</a>, arXiv:1803.04041 [math.PR], 2018.
%F A088534(a(n)) > 1. - _Reinhard Zumkeller_, Oct 30 2011
%e a(2) = 91 = 1^2 + 1*9 + 9^2 = 5^2 + 5*6 + 6^2;
%e a(45) = 931 = 1^2+1*30+30^2 = 9^2+9*25+25^2 = 14^2+14*21+21^2;
%e a(97) = 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. - _Reinhard Zumkeller_, Oct 30 2011
%t amax = 2000; 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 A118886 = Select[Range[0, 3 xmax^2], # <= amax && f[#] > 1&] (* _Jean-François Alcover_, Jun 21 2018 *)
%o (Haskell)
%o a118886 n = a118886_list !! (n-1)
%o a118886_list = filter ((> 1) . a088534) a003136_list
%o -- _Reinhard Zumkeller_, Oct 30 2011
%o (PARI) is(n)=#bnfisintnorm(bnfinit(z^2+z+1), n) > 2;
%o select(is, vector(1500,j,j)) \\ _Joerg Arndt_, Jan 11 2015
%o (Julia)
%o function isA118886(n)
%o n < 49 && return false
%o n % 3 == 2 && return false
%o M = Int(round(2*sqrt(n/3)))
%o count = 0
%o for y in 0:M, x in 0:y
%o n == x^2 + y^2 + x*y && (count += 1)
%o count == 2 && break
%o end
%o return count >= 2
%o end
%o A118886list(upto) = [n for n in 0:upto if isA118886(n)]
%o A118886list(1099) |> println # _Peter Luschny_, Mar 17 2018
%Y Subsequence of Loeschian numbers A003136.
%Y Complement of A198772 with respect to A003136.
%Y Subsequences: A198773, A198774, A198775.
%Y Cf. A024606, A118882.
%K nonn
%O 1,1
%A _Franklin T. Adams-Watters_, May 03 2006