A352316 Perimeter of primitive integer-sided triangles such that the distance d = OI between the circumcenter O and the incenter I is also a positive integer.

36, 128, 120, 288, 360, 500, 1008, 972, 1024, 1500, 1152, 1372, 2520, 3072, 2520, 3960, 4000, 4116, 4860, 5040, 4500, 5760, 6860, 5324, 6804, 6435, 8000, 7776, 8192, 10920, 8788, 9216, 10395, 10976

Offset

1,1

Comments

For the corresponding primitive triples, miscellaneous properties and links, see A352314.

The sequence is not increasing. For example, a(2) = 128 for triangle with largest side = 48 while a(3) = 120 for triangle with largest side = 55.

Links

Table of n, a(n) for n=1..34.

Formula

a(n) = A352314(n, 1) + A352314(n, 2) + A352314(n, 3).

Example

a(1) = 36 because the smallest triple is (10, 10, 16) with corresponding d = OI = A352315(1) = 5.

Crossrefs

Cf. A231174, A350378, A350379, A352314, A352315.

Sequence in context: A365506 A250625 A057837 * A007265 A260130 A155708

Adjacent sequences: A352313 A352314 A352315 * A352317 A352318 A352319

Keyword

nonn,more

Author

Bernard Schott, Mar 14 2022

Extensions

a(19)-a(34) from Jinyuan Wang, Mar 14 2022

Status

approved