A070147 -id:A070147 - cp's OEIS frontend

A070141 Number of obtuse integer triangles with perimeter n having integral area.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 4, 0, 0, 0, 1, 0, 2

Offset: 1

Reinhard Zumkeller, May 05 2002

nonn

a(n) = A051516(n) - A070140(n) - A024155(n).

Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Obtuse Triangle.
R. Zumkeller, Integer-sided triangles

Cf. A051516, A070101, A070147.

A070146 Numbers n such that [A070080(n), A070081(n), A070082(n)] is an acute integer triangle with integer area.

Original entry on oeis.org

39, 269, 375, 587, 862, 972, 1196, 1955, 1988, 2352, 2555, 2796, 3818, 4319, 4406, 5378, 6522, 6808, 6880, 6890, 6921, 7234, 7360, 8193, 9159, 9207, 10272, 14545, 15004, 15061, 15101, 15216, 15237, 15943, 16502

Offset: 1

Reinhard Zumkeller, May 05 2002

nonn

			a(1)=39: [A070080(39), A070081(39), A070082(39)] = [5,5,6]: A070085(39)=5^2+5^2-6^2=14>0 and area^2 = s*(s-5)*(s-5)*(s-6) with s=A070083(39)/2=(5+5+6)/2=8, area^2=8*3*3*2=16*9 is an integer square, therefore A070086(39)=area=4*3=12.

Eric Weisstein's World of Mathematics, Heronian Triangle.
Eric Weisstein's World of Mathematics, Acute Triangle.
R. Zumkeller, Integer-sided triangles

Cf. A070142, A070136, A070147, A070140.

cp's OEIS Frontend

A070141 Number of obtuse integer triangles with perimeter n having integral area.

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