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%I #11 May 27 2013 05:07:25
%S 1,1,2,1,1,1,1,1,3,2,1,1,1,1,1,1,1,4,1,1,1,1,1,2,1,2,1,1,1,1,3,1,1,5,
%T 1,1,1,2,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,6,1,1,1,1,1,1,1,1,1,1,1,1,1,4,
%U 1,1,2,1,1,1,1,3,1,1,1,1,1,3,1,7,2,1,2,1,1,1
%N Greatest common divisor of sides of integer triangles [A070080(n), A070081(n), A070082(n)], sorted by perimeter, sides lexicographically ordered.
%C a(n)>1 iff there exists a smaller similar triangle [A070080(k), A070081(k), A070082(k)] with k<n and A070080(n)=A070080(k)*a(n), A070081(n)=A070081(k)*a(n) and A070082(n)=A070082(k)*a(n).
%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%F a(n) = GCD(A070080(n), A070081(n), A070082(n)).
%t maxPer = 22; maxSide = Floor[(maxPer - 1)/2]; order[{a_, b_, c_}] := (a + b + c)*maxPer^3 + a*maxPer^2 + b*maxPer + c; triangles = Reap[Do[If[a + b + c <= maxPer && c - b < a < c + b && b - a < c < b + a && c - a < b < c + a, Sow[{a, b, c}]], {a, 1, maxSide}, {b, a, maxSide}, {c, b, maxSide}]][[2, 1]]; GCD @@@ Sort[triangles, order[#1] < order[#2] &] (* _Jean-François Alcover_, May 27 2013 *)
%Y Cf. A051493, A005044, A070091, A070094, A070102, A070109, A070110, A070113, A070116, A070119, A070128, A070137.
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, May 05 2002
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