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%I #18 Dec 11 2021 04:35:54
%S 1260,2520,2574,3080,3740,3780,3978,4620,4940,5148,5720,5814,5940,
%T 6435,6930,7020,7280,7560,7820,7866,7956,8190,8550,8580,8892,9044,
%U 10010,10350,10395,10472,10640,11628,11880,12006,12240,12870,12920,13050,13260,13340,13680,13685,13832,13860,13950
%N Perimeters of more than one primitive 60-degree integer triangle.
%H Seiichi Manyama, <a href="/A350039/b350039.txt">Table of n, a(n) for n = 1..10000</a>
%e 399^2 + 440^2 - 399*440 = 421^2, 56^2 + 615^2 - 56*615 = 589^2 and 399 + 440 + 421 = 56 + 615 + 589 = 1260. So 1260 is a term.
%e 5159^2 + 5904^2 - 5159*5904 = 5569^2, 3344^2 + 7119^2 - 3344*7119 = 6169^2, 1287^2 + 7952^2 - 1287*7952 = 7393^2 and 5159 + 5904 + 5569 = 3344 + 7119 + 6169 = 1287 + 7952 + 7393 = 16632. So 16632 is a term.
%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 x, y, z = j * j, i * j, i * i
%o ary << 2 * x + 5 * y + 2 * z
%o ary << 3 * x + 3 * y
%o end
%o }
%o }
%o ary
%o end
%o p A(100).group_by(&:to_i).select{|k, v| v.size > 1}.keys.sort[0..50]
%Y Cf. A024408, A242039, A350038.
%K nonn
%O 1,1
%A _Seiichi Manyama_, Dec 10 2021
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