A070113 Numbers k such that [A070080(k), A070081(k), A070082(k)] is a scalene integer triangle with relatively prime side lengths.

8, 13, 17, 20, 21, 25, 29, 30, 33, 36, 37, 41, 42, 44, 45, 49, 53, 56, 57, 59, 60, 62, 66, 67, 69, 70, 74, 75, 77, 78, 79, 80, 83, 86, 89, 90, 92, 96, 97, 99, 100, 101, 102, 105, 106, 110, 111, 113, 114, 115, 119, 122, 123, 125, 126

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Examples

			36 is a term [A070080(36), A070081(36), A070082(36)]=[3<6<7], A070084(36)=gcd(3,6,7)=1.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..596
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

Cf. A005044, A070122, A070131, A070112, A070110.

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 < b < c && GCD[a, b, c] == 1] // Flatten (* Jean-François Alcover, Oct 04 2021 *)