login
A070110
Numbers k such that [A070080(k), A070081(k), A070082(k)] is an integer triangle with relatively prime side lengths.
14
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
1,2
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.
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..789
Reinhard Zumkeller, Integer-sided triangles
EXAMPLE
13 is a term: [A070080(13), A070081(13), A070082(13)]=[2,4,5], A070084(13)=gcd(2,4,5)=1.
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 *)
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved