A350045 - OEIS

%I #17 Dec 12 2021 02:16:23

%S 15,28,40,66,77,91,104,126,144,153,170,187,190,209,220,228,260,276,

%T 286,299,322,325,345,350,390,400,420,435,442,464,476,493,496,522,527,

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

%H Seiichi Manyama, <a href="/A350045/b350045.txt">Table of n, a(n) for n = 1..10000</a>

%e b(n) = Sum_{k=1..3} A264827(3*n+k-3).

%e b(1) = 3+5+7 = 15 = a(1).

%e b(2) = 5+16+19 = 40 = a(3).

%e b(3) = 7+8+13 = 28 = a(2).

%e b(4) = 7+33+37 = 77 = a(5).

%e b(5) = 9+56+61 = 126 = a(8).

%e b(6) = 11+24+31 = 66 = a(4).

%e b(7) = 11+85+91 = 187 = a(12).

%e b(8) = 13+35+43 = 91 = a(6).

%o (Ruby)

%o def A(n)

%o   ary = []

%o   (1..n).each{|i|

%o     (i + 1..n).each{|j|

%o       if i.gcd(j) == 1 && (i - j) % 3 > 0

%o         ary << 2 * j * j + 3 * i * j + i * i

%o       end

%o     }

%o   }

%o   ary

%o end

%o p A(30).uniq.sort[0..100]

%Y Cf. A002476, A264827, A350038, A350047.

%K nonn

%O 1,1

%A _Seiichi Manyama_, Dec 11 2021