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 A024406 Ordered areas of primitive Pythagorean triangles. 26
 6, 30, 60, 84, 180, 210, 210, 330, 504, 546, 630, 840, 924, 990, 1224, 1320, 1386, 1560, 1710, 1716, 2310, 2340, 2574, 2730, 2730, 3036, 3570, 3900, 4080, 4290, 4620, 4914, 5016, 5610, 5814, 6090, 6630, 7140, 7440, 7854, 7956, 7980, 7980, 8970, 8976, 9690 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence also gives Fibonacci's congruous numbers (or congrua) divided by 4 with multiplicities, not regarding leg exchange in the underlying primitive Pythagorean triangle. See A258150 and the example. - Wolfdieter Lang, Jun 14 2015 The squarefree part of an entry which is not squarefree is a primitive congruent number from A006991 belonging to a Pythagorean triangle with rational (not all integer) side lengths (and its companion obtained by exchanging the legs). See the W. Lang link. - Wolfdieter Lang, Oct 25 2016 LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 Ron Knott, Pythagorean Triples and Online Calculators Wolfdieter Lang, Non-squarefree entries, their congruent numbers and rational Pythagorean triangles Eric Weisstein's World of Mathematics, Congruum Problem FORMULA a(n) = 6*A020885(n). - Lekraj Beedassy, Apr 30 2004 a(n) = A121728(n)*A121729(n)/2. - M. F. Hasler, Apr 16 2020 EXAMPLE a(6) = a(7) = 210 corresponds to the area (in some squared length unit) of the primitive Pythagorean triangles (21, 20, 29) and (35, 12, 37). Fibonacci's congruum C = 840 = 210*4 belongs to the two triples [x, y, z] = [29, 41, 1] and [37, 47, 23], solving x^2 + C = y^2 and x^2 - C = z^2. - Wolfdieter Lang, Jun 14 2015 a(5) = 180 = 6^2*5 lead to the primitive congruent number A006991(1) = 5 from the primitive Pythagorean triangle [9, 40, 41] after division by 6: [3/2, 20/3, 41/6]. See the link for the other nonsquarefree a(n) numbers. - Wolfdieter Lang, Oct 25 2016 CROSSREFS Cf. A009112, A024365, A094182, A094183, A256418 (congrua), A258150. Sequence in context: A014203 A044083 A239978 * A024365 A057229 A120734 Adjacent sequences: A024403 A024404 A024405 * A024407 A024408 A024409 KEYWORD nonn,easy AUTHOR David W. Wilson STATUS approved

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Last modified June 10 19:34 EDT 2023. Contains 363207 sequences. (Running on oeis4.)