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A350045 Numbers that are the perimeter of a primitive 120-degree integer triangle.

%I A350045 #17 Dec 12 2021 02:16:23
%S A350045 15,28,40,66,77,91,104,126,144,153,170,187,190,209,220,228,260,276,
%T A350045 286,299,322,325,345,350,390,400,420,435,442,464,476,493,496,522,527,
%U A350045 544,551,558,589,608,620,630,646,665,672,703,714,740,770,777,798,805,814,840,851,861,874,888,902,920,943,946,950
%N A350045 Numbers that are the perimeter of a primitive 120-degree integer triangle.
%H A350045 Seiichi Manyama, <a href="/A350045/b350045.txt">Table of n, a(n) for n = 1..10000</a>
%e A350045 b(n) = Sum_{k=1..3} A264827(3*n+k-3).
%e A350045 b(1) = 3+5+7 = 15 = a(1).
%e A350045 b(2) = 5+16+19 = 40 = a(3).
%e A350045 b(3) = 7+8+13 = 28 = a(2).
%e A350045 b(4) = 7+33+37 = 77 = a(5).
%e A350045 b(5) = 9+56+61 = 126 = a(8).
%e A350045 b(6) = 11+24+31 = 66 = a(4).
%e A350045 b(7) = 11+85+91 = 187 = a(12).
%e A350045 b(8) = 13+35+43 = 91 = a(6).
%o A350045 (Ruby)
%o A350045 def A(n)
%o A350045   ary = []
%o A350045   (1..n).each{|i|
%o A350045     (i + 1..n).each{|j|
%o A350045       if i.gcd(j) == 1 && (i - j) % 3 > 0
%o A350045         ary << 2 * j * j + 3 * i * j + i * i
%o A350045       end
%o A350045     }
%o A350045   }
%o A350045   ary
%o A350045 end
%o A350045 p A(30).uniq.sort[0..100]
%Y A350045 Cf. A002476, A264827, A350038, A350047.
%K A350045 nonn
%O A350045 1,1
%A A350045 _Seiichi Manyama_, Dec 11 2021