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

15, 28, 40, 66, 77, 91, 104, 126, 144, 153, 170, 187, 190, 209, 220, 228, 260, 276, 286, 299, 322, 325, 345, 350, 390, 400, 420, 435, 442, 464, 476, 493, 496, 522, 527, 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

Offset: 1

Author

Seiichi Manyama, Dec 11 2021

Keywords

• nonn

Examples

			b(n) = Sum_{k=1..3} A264827(3*n+k-3).
b(1) = 3+5+7 = 15 = a(1).
b(2) = 5+16+19 = 40 = a(3).
b(3) = 7+8+13 = 28 = a(2).
b(4) = 7+33+37 = 77 = a(5).
b(5) = 9+56+61 = 126 = a(8).
b(6) = 11+24+31 = 66 = a(4).
b(7) = 11+85+91 = 187 = a(12).
b(8) = 13+35+43 = 91 = a(6).
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002476, A264827, A350038, A350047.

Programs

Ruby

def A(n)
  ary = []
  (1..n).each{|i|
    (i + 1..n).each{|j|
      if i.gcd(j) == 1 && (i - j) % 3 > 0
        ary << 2 * j * j + 3 * i * j + i * i
      end
    }
  }
  ary
end
p A(30).uniq.sort[0..100]