A291420 Numbers n such that there exist exactly four distinct Pythagorean triangles, at least one of them primitive, with area n.

341880, 8168160, 14636160, 17957940, 52492440, 116396280, 1071572040, 1187525640, 1728483120, 5988702720, 6609482880, 22539095040, 29239970760, 136496680320, 258670630680, 398648544840, 494892478080, 592003418160, 1329673884000, 1343798407560, 2190884461920

Offset

1,1

Comments

Numbers n such that there exist positive integers x, y with x > y and n = x*y*(x-y)*(x+y).

Many of them consist of a Pythagorean triangle plus a triple which is a solution to Carroll's problem: Find three Pythagorean triangles with the same area.

Links

Table of n, a(n) for n=1..21.

Example

p^2 - p*q + q^2 = r^2;
p = 208, q = 418, r = 362, q - p = 210;
n = p*r*q*(q-p) = 208*418*362*210 = 6609482880.
x = 640, y = 627 gives the same area:
n = x*y*(x-y)*(x+y) = 640*627*13*1267 = 6609482880.

Crossrefs

Cf. A009127, A024407, A055193, A088513, A088977, A089025, A177021, A291591.

Sequence in context: A151563 A251495 A233596 * A266171 A233604 A363175

Adjacent sequences: A291417 A291418 A291419 * A291421 A291422 A291423

Keyword

nonn

Author

Sture Sjöstedt, Aug 23 2017

Extensions

a(12)-a(21) from Giovanni Resta, Aug 28 2017

Status

approved