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Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle with integer area.
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%I #11 Feb 16 2025 08:32:46

%S 52,252,368,372,561,659,839,957,1156,1186,1204,1582,1912,1920,1971,

%T 2115,2713,2774,2790,3251,3473,3728,3746,4286,4307,4313,4330,5008,

%U 5272,5374,6369,6389,6432,6776,6881,7223,7310,7341

%N Numbers n such that [A070080(n), A070081(n), A070082(n)] is an obtuse integer triangle with integer area.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ObtuseTriangle.html">Obtuse Triangle</a>.

%H R. Zumkeller, <a href="/A070080/a070080.txt">Integer-sided triangles</a>

%e a(1)=52: [A070080(52), A070081(52), A070082(52)] = [5,5,8]: A070085(52)=5^2+5^2-8^2=-14<0 and area^2 = s*(s-5)*(s-5)*(s-6) with s=A070083(52)/2=(5+5+8)/2=9, area^2=9*4*4*1=16*9 is an integer square, therefore A070086(52)=area=4*3=12.

%Y Cf. A070142, A070136, A070146, A070141.

%K nonn,changed

%O 1,1

%A _Reinhard Zumkeller_, May 05 2002