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A350047 Perimeters of more than one primitive 120-degree integer triangle.

%I A350047 #15 Dec 12 2021 02:16:14
%S A350047 2730,4080,7590,9044,11704,12180,13020,13485,13920,14880,15810,16100,
%T A350047 18870,21090,22755,23370,24752,25172,26445,27060,28380,29670,30315,
%U A350047 31020,32430,32890,33810,34545,34580,36660,37950,38038,38220,38955,41340,42476,44520,46046,46110
%N A350047 Perimeters of more than one primitive 120-degree integer triangle.
%H A350047 Seiichi Manyama, <a href="/A350047/b350047.txt">Table of n, a(n) for n = 1..10000</a>
%e A350047 897^2 + 560^2 + 897*560 = 1273^2, 168^2 + 1235^2 + 168*1235 = 1327^2 and 897 + 560 + 1273 = 168 + 1235 + 1327 = 2730. So 2730 is a term.
%e A350047 38640^2 + 5291^2 + 38640*5291 = 41539^2, 23088^2 + 22715^2 + 23088*22715 = 39667^2, 10857^2 + 34040^2 + 10857*34040 = 40573^2 and 38640 + 5291 + 41539 = 23088 + 22715 + 39667 = 10857 + 34040 + 40573 = 85470. So 85470 is a term.
%o A350047 (Ruby)
%o A350047 def A(n)
%o A350047   ary = []
%o A350047   (1..n).each{|i|
%o A350047     (i + 1..n).each{|j|
%o A350047       if i.gcd(j) == 1 && (i - j) % 3 > 0
%o A350047         ary << 2 * j * j + 3 * i * j + i * i
%o A350047       end
%o A350047     }
%o A350047   }
%o A350047   ary
%o A350047 end
%o A350047 p A(200).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]
%Y A350047 Cf. A350039, A350045.
%K A350047 nonn
%O A350047 1,1
%A A350047 _Seiichi Manyama_, Dec 11 2021