A070110 Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with relatively prime side lengths.

1, 2, 4, 5, 6, 7, 8, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 32, 33, 35, 36, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 72, 73, 74, 75, 77

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Comments

A070084(a(k)) = gcd(A070080(a(k)), A070081(a(k)), A070082(a(k))) = 1;

all integer triangles [A070080(a(k)), A070081(a(k)), A070082(a(k))] are mutually nonisomorphic.

Examples

			13 is a term: [A070080(13), A070081(13), A070082(13)]=[2,4,5], A070084(13)=gcd(2,4,5)=1.
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 1..789
• Reinhard Zumkeller, Integer-sided triangles

Crossrefs

Cf. A051493, A070113, A070116, A070119, A070122, A070125, A070128, A070131, A070134, A070137, A070084.

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