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A070115 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an isosceles integer triangle.

%I A070115 #12 Oct 12 2021 21:57:02
%S A070115 1,2,3,4,5,6,7,9,10,11,12,14,15,16,18,19,22,23,24,26,27,28,31,32,34,
%T A070115 35,38,39,40,43,46,47,48,51,52,54,55,58,61,63,64,65,68,71,72,73,76,81,
%U A070115 82,84,85,88,91,93,94,95,98,103,104,107,108
%N A070115 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an isosceles integer triangle.
%H A070115 Jean-François Alcover, <a href="/A070115/b070115.txt">Table of n, a(n) for n = 1..365</a>
%H A070115 Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%e A070115 26 is a term because [A070080(26), A070081(26), A070082(26)] = [4=4<6].
%t A070115 m = 55 (* max perimeter *);
%t A070115 sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
%t A070115 triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1]& // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
%t A070115 Position[triangles, {a_, a_, b_} | {a_, b_, b_}] // Flatten (* _Jean-François Alcover_, Oct 12 2021 *)
%Y A070115 Cf. A059169, A070116, A070117, A070124, A070125, A070126, A070133, A070134, A070135.
%K A070115 nonn
%O A070115 1,2
%A A070115 _Reinhard Zumkeller_, May 05 2002