A070118 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an acute integer triangle.

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, 40, 43, 45, 46, 47, 48, 51, 53, 54, 55, 58, 60, 63, 64, 65, 68, 70, 71, 72, 73, 76, 81, 83, 84, 85, 88, 90, 92, 93, 94, 95, 98, 103, 106, 107, 108

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Examples

			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.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..431
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

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

Programs

Mathematica

m = 50; (* max perimeter *)
sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
Position[triangles, {a_, b_, c_} /; a^2 + b^2 - c^2 > 0] // Flatten (* Jean-François Alcover, Oct 04 2021 *)