login
A070127
Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle.
11
5, 8, 13, 14, 20, 21, 25, 26, 29, 30, 32, 36, 37, 41, 42, 44, 49, 50, 52, 56, 57, 59, 61, 62, 66, 67, 69, 74, 75, 77, 78, 79, 80, 82, 86, 87, 89, 91, 96, 97, 99, 100, 101, 102, 104, 105, 110, 111, 113, 115, 118, 122, 123, 125, 126, 127
OFFSET
1,1
LINKS
Jean-François Alcover, Table of n, a(n) for n = 1..724
EXAMPLE
a(10)=30: [A070080(30), A070081(30), A070082(30)]=[3,5,7], A070085(30)=3^2+5^2-7^2=9+25-49=-15<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^2 + b^2 - c^2 < 0] // Flatten (* Jean-François Alcover, Oct 11 2021 *)
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, May 05 2002
STATUS
approved