

A291420


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


0



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

1,1


COMMENTS

Numbers n such that there exist positive integers x, y with x > y and n = x*y*(xy)*(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*(qp) = 208*418*362*210 = 6609482880.
x = 640, y = 627 gives the same area:
n = x*y*(xy)*(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 A029568
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



