A070122 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an acute scalene integer triangle with relatively prime side lengths.

33, 45, 53, 60, 70, 83, 90, 92, 106, 114, 119, 132, 134, 142, 148, 162, 165, 168, 175, 181, 183, 197, 200, 203, 204, 218, 224, 237, 240, 245, 247, 261, 264, 267, 268, 282, 290, 293, 296, 309, 316, 317, 319, 333, 341, 345, 348

Offset

1,1

Links

Jean-François Alcover, Table of n, a(n) for n = 1..229

Reinhard Zumkeller, Integer-sided triangles

Example

70 is a term because [A070080(70), A070081(70), A070082(70)]=[5<7<8], A070084(70)=gcd(5,7,8)=1, A070085(70)=5^2+7^2-8^2=25+49-64=10>0.

Mathematica

m = 55 (* 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 < b < c && GCD[a, b, c] == 1 && a^2 + b^2 - c^2 > 0] // Flatten (* Jean-François Alcover, Oct 12 2021 *)

Crossrefs

Cf. A070096, A070118, A070110, A070112.

Sequence in context: A050875 A060876 A070121 * A247527 A111458 A179244

Adjacent sequences: A070119 A070120 A070121 * A070123 A070124 A070125

Keyword

nonn

Author

Reinhard Zumkeller, May 05 2002

Status

approved