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

2730, 4080, 7590, 9044, 11704, 12180, 13020, 13485, 13920, 14880, 15810, 16100, 18870, 21090, 22755, 23370, 24752, 25172, 26445, 27060, 28380, 29670, 30315, 31020, 32430, 32890, 33810, 34545, 34580, 36660, 37950, 38038, 38220, 38955, 41340, 42476, 44520, 46046, 46110

Offset: 1

Author

Seiichi Manyama, Dec 11 2021

Keywords

• nonn

Examples

			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.
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.
		

Links

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

Crossrefs

Cf. A350039, A350045.

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(200).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]