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A070118
Numbers n such that [A070080(n), A070081(n), A070082(n)] is an acute integer triangle.
11
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
1,2
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..431
Reinhard Zumkeller, Integer-sided triangles
EXAMPLE
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.
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 *)
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved