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 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 (list; graph; refs; listen; history; text; internal format)
 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 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 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

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Last modified March 20 16:59 EDT 2018. Contains 300989 sequences. (Running on oeis4.)