cp's OEIS Frontend

A070112 Numbers n such that [A070080(n), A070081(n), A070082(n)] is a scalene integer triangle.

%I A070112 #12 Oct 12 2021 21:56:53
%S A070112 8,13,17,20,21,25,29,30,33,36,37,41,42,44,45,49,50,53,56,57,59,60,62,
%T A070112 66,67,69,70,74,75,77,78,79,80,83,86,87,89,90,92,96,97,99,100,101,102,
%U A070112 105,106,110,111,113,114,115,116,119,122
%N A070112 Numbers n such that [A070080(n), A070081(n), A070082(n)] is a scalene integer triangle.
%H A070112 Jean-François Alcover, <a href="/A070112/b070112.txt">Table of n, a(n) for n = 1..920</a>
%H A070112 Reinhard Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>
%e A070112 a(17)=50: [A070080(50), A070081(50), A070082(50)]=[4<6<8].
%t A070112 m = 55 (* max perimeter *);
%t A070112 sides[per_] := Select[Reverse /@ IntegerPartitions[per, {3}, Range[ Ceiling[per/2]]], #[[1]] < per/2 && #[[2]] < per/2 && #[[3]] < per/2 &];
%t A070112 triangles = DeleteCases[Table[sides[per], {per, 3, m}], {}] // Flatten[#, 1] & // SortBy[Total[#] m^3 + #[[1]] m^2 + #[[2]] m + #[[1]] &];
%t A070112 Position[triangles, {a_, b_, c_} /; a < b < c] // Flatten (* _Jean-François Alcover_, Oct 12 2021 *)
%Y A070112 Cf. A005044, A070113, A070114, A070121, A070122, A070123, A070130, A070131, A070132.
%K A070112 nonn
%O A070112 1,1
%A A070112 _Reinhard Zumkeller_, May 05 2002