A070784 -id:A070784 - cp's OEIS frontend

A070786 Area of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

1, 1, 2, 2, 1, 3, 1, 2, 3, 4, 3, 2, 1, 3, 3, 6, 2, 4, 2, 4, 6, 1, 3, 5, 2, 4, 3, 6, 2, 3, 1, 5, 1, 4, 4, 2, 6, 7, 3, 6, 8, 6, 3, 1, 3, 5, 6, 4, 8, 2, 5, 10, 1, 4, 2, 6, 3, 7, 9, 5, 9, 7, 3, 2, 4, 1, 8, 9, 5, 7, 10, 3, 6, 9, 12, 4, 2, 8, 6, 4, 2, 10, 8, 12, 6, 2, 6, 3, 1, 7, 5, 10, 11, 4, 8, 7, 14, 3, 6, 3

Offset: 1

Henry Bottomley, May 07 2002

nonn

			a(6)=3 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

A. Bogomolny, Sam Loyd's Geometric Puzzle

Cf. A055595, A070783, A070784, A070785, A070787.

A070787 Number of triangles with sides whose squares are integers and with positive integer area and longest side of length sqrt(n).

Original entry on oeis.org

0, 0, 0, 1, 2, 0, 0, 2, 1, 4, 0, 1, 3, 0, 2, 5, 5, 2, 0, 13, 0, 0, 0, 2, 9, 8, 1, 1, 9, 4, 0, 10, 0, 10, 2, 12, 11, 0, 3, 23, 14, 0, 0, 1, 13, 0, 0, 5, 5, 18, 5, 32, 18, 2, 2, 2, 0, 19, 0, 13, 16, 0, 1, 20, 35, 0, 0, 42, 0, 4, 0, 23, 24, 23, 9, 1, 0, 8, 0, 44, 10, 27, 0, 1, 48, 0, 9, 2, 27, 25, 3

Offset: 1

Henry Bottomley, May 07 2002

nonn

			a(13)=3 since the 3 triangles with sides {sqrt(13), sqrt(5), sqrt(4)}, {sqrt(13), sqrt(8), sqrt(1)} and {sqrt(13), sqrt(9), sqrt(4)} have areas 2, 1 and 3 respectively.

A. Bogomolny, Sam Loyd's Geometric Puzzle

Cf. A054875, A070783, A070784, A070785, A070786.

A070783 Square of longest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

4, 5, 5, 8, 8, 9, 10, 10, 10, 10, 12, 13, 13, 13, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24, 24, 25, 25, 25, 25, 25, 25, 25, 25, 25, 26, 26, 26, 26, 26, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 29, 29, 29, 29

Offset: 1

Henry Bottomley, May 07 2002

nonn

			a(6)=9 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

A. Bogomolny, Sam Loyd's Geometric Puzzle

Cf. A055592, A070784, A070785, A070786, A070787.

A070785 Square of shortest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

Original entry on oeis.org

2, 1, 4, 4, 1, 5, 2, 2, 4, 8, 6, 4, 1, 4, 3, 12, 5, 8, 2, 5, 13, 4, 5, 8, 1, 4, 4, 10, 4, 5, 2, 10, 1, 5, 4, 1, 9, 13, 2, 8, 16, 12, 3, 5, 4, 8, 9, 4, 16, 1, 5, 20, 4, 8, 2, 8, 2, 10, 18, 4, 15, 14, 8, 4, 5, 1, 13, 17, 4, 8, 16, 6, 6, 12, 24, 10, 5, 16, 9, 4, 1, 17, 10, 26, 5, 8, 10, 4, 2, 10, 4

Offset: 1

Henry Bottomley, May 07 2002

nonn

			a(6)=5 since the triangle with sides sqrt(9), sqrt(8) and sqrt(5) has area 3.

A. Bogomolny, Sam Loyd's Geometric Puzzle

Cf. A055594, A070783, A070784, A070786, A070787.

cp's OEIS Frontend

A070786 Area of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

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A070787 Number of triangles with sides whose squares are integers and with positive integer area and longest side of length sqrt(n).

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A070783 Square of longest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

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A070785 Square of shortest side of triangles with sides whose squares are integers and with positive integer area, ordered by longest side, then second longest side and finally shortest side.

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