A070138 Number of integer triangles with an integer area having relatively prime sides a, b and c such that a + b + c = n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 3, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 5, 0, 0, 0, 0, 0, 3

Offset: 1

Author

Reinhard Zumkeller, May 05 2002

Keywords

• nonn

Comments

From Peter Kagey, Jan 30 2018: (Start)

a(k) > 0 if and only if k is in A096468.

Records appear at indices 12, 36, 54, 84, 98, 162, 242, 338, 484, 578, ....

a(2k - 1) = 0 for all integers k > 0.

(End)

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Heronian Triangle.
• R. Zumkeller, Integer-sided triangles

Crossrefs

Cf. A051493, A051516, A070088, A070109, A070143, A096468, A239246.

Extensions

Corrected by T. D. Noe, Jun 17 2004