A350038 Numbers that are the perimeter of a primitive 60-degree integer triangle.

18, 20, 35, 36, 45, 56, 77, 84, 90, 104, 110, 120, 126, 135, 143, 170, 176, 182, 189, 198, 209, 210, 216, 221, 252, 260, 264, 266, 270, 272, 273, 297, 299, 323, 350, 351, 360, 368, 374, 378, 380, 390, 396, 425, 432, 437, 459, 462, 464, 468, 476, 494, 495, 506, 527, 551, 561, 570, 575, 585, 594, 608, 612

Offset: 1

Author

Seiichi Manyama, Dec 10 2021

Keywords

• nonn

Examples

			b(n) = Sum_{k=1..3} A264826(3*n+k-3).
c(n) = Sum_{k=1..3} A201223(3*n+k-3).
b(1) = c(1) = 3+7+8 = 18 = a(1).
b(2) = c(2) = 5+7+8 = 20 = a(2).
b(3) = c(5) = 5+19+21 = 45 = a(5).
b(4) = c(3) = 7+13+15 = 35 = a(3).
b(5) = c(9) = 7+37+40 = 84 = a(8).
b(6) = c(4) = 8+13+15 = 36 = a(4).
		

Links

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

Crossrefs

Cf. A024364, A201223, A264826, A350013, A350039.

Programs

Ruby

def A(n)
  ary = []
  (1..n).each{|i|
    (i + 1..n).each{|j|
      if i.gcd(j) == 1 && (i - j) % 3 > 0
        x, y, z = j * j, i * j, i * i
        ary << 2 * x + 5 * y + 2 * z
        ary << 3 * x + 3 * y
      end
    }
  }
  ary
end
p A(20).uniq.sort[0..100]