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A070122 Numbers m such that [A070080(m), A070081(m), A070082(m)] is an acute scalene integer triangle with relatively prime side lengths. 8
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 29 18:25 EDT 2022. Contains 354913 sequences. (Running on oeis4.)