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A024406
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Ordered areas of primitive Pythagorean triangles.
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26
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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
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FORMULA
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a(n) = 6*A020885(n). - Lekraj Beedassy, Apr 30 2004
a(n) = A121728(n)*A121729(n)/2. - M. F. Hasler, Apr 16 2020
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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David W. Wilson
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STATUS
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approved
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