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A070137
Numbers k such that [A070080(k), A070081(k), A070082(k)] is a right integer triangle with relatively prime side lengths.
5
17, 212, 493, 1297, 2574, 4298, 5251, 14414, 16365, 21231, 26125, 39056, 42597, 55042, 63770, 75052, 91121, 97256, 124355, 164640, 200999, 213083, 253721, 275999, 367997, 384154, 415778, 478343, 511633, 518370, 606417, 665040, 689356, 755435, 846571
OFFSET
1,1
COMMENTS
Right integer triangles have integer areas: see A070143.
LINKS
Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Right Triangle.
Reinhard Zumkeller, Integer-sided triangles
EXAMPLE
493 is a term: [A070080(493), A070081(493), A070082(493)]=[8,15,17], A070084(493)=gcd(8,15,17)=1, A070085(493)=8^2+15^2-17^2=64+225-289=0.
MATHEMATICA
m = 500 (* 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 && a^2 + b^2 - c^2 == 0] // Flatten (* Jean-François Alcover, Oct 04 2021 *)
CROSSREFS
Sequence in context: A016299 A016250 A255819 * A021054 A016246 A009441
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
EXTENSIONS
More terms from Jean-François Alcover, Oct 04 2021
STATUS
approved