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%I #17 Oct 06 2021 02:40:27
%S 8,13,17,20,21,25,29,30,33,36,37,41,42,44,45,49,53,56,57,59,60,62,66,
%T 67,69,70,74,75,77,78,79,80,83,86,89,90,92,96,97,99,100,101,102,105,
%U 106,110,111,113,114,115,119,122,123,125,126
%N Numbers k such that [A070080(k), A070081(k), A070082(k)] is a scalene integer triangle with relatively prime side lengths.
%H Jean-François Alcover, <a href="/A070113/b070113.txt">Table of n, a(n) for n = 1..596</a>
%H Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%e 36 is a term [A070080(36), A070081(36), A070082(36)]=[3<6<7], A070084(36)=gcd(3,6,7)=1.
%t m = 50 (* max perimeter *);
%t sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
%t triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
%t Position[triangles, {a_, b_, c_} /; a < b < c && GCD[a, b, c] == 1] // Flatten (* _Jean-François Alcover_, Oct 04 2021 *)
%Y Cf. A005044, A070122, A070131, A070112, A070110.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, May 05 2002
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