A070118 - OEIS

%I #13 Oct 04 2021 07:59:20

%S 1,2,3,4,6,7,9,10,11,12,15,16,18,19,22,23,24,27,28,31,33,34,35,38,39,

%T 40,43,45,46,47,48,51,53,54,55,58,60,63,64,65,68,70,71,72,73,76,81,83,

%U 84,85,88,90,92,93,94,95,98,103,106,107,108

%N Numbers n such that [A070080(n), A070081(n), A070082(n)] is an acute integer triangle.

%H Jean-François Alcover, <a href="/A070118/b070118.txt">Table of n, a(n) for n = 1..431</a>

%H Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%e a(21)=33: [A070080(33), A070081(33), A070082(33)]=[4,5,6], A070085(33)=4^2+5^2-6^2=16+25-36=5>0.

%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^2 + b^2 - c^2 > 0] // Flatten (* _Jean-François Alcover_, Oct 04 2021 *)

%Y Cf. A070093, A070119, A070120, A070121, A070122, A070123, A070124, A070125, A070126.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, May 05 2002