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 A020885 Ordered areas (divided by 6) of primitive Pythagorean triangles (with multiple entries). 10
 1, 5, 10, 14, 30, 35, 35, 55, 84, 91, 105, 140, 154, 165, 204, 220, 231, 260, 285, 286, 385, 390, 429, 455, 455, 506, 595, 650, 680, 715, 770, 819, 836, 935, 969, 1015, 1105, 1190, 1240, 1309, 1326, 1330, 1330, 1495, 1496, 1615, 1729, 1771, 1785, 1820, 1925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Since squares are 0 or 1 under both mod 3 and mod 4, for the Pythagorean equation A^2 + B^2 = C^2 to hold, each of 3 and 4 divides either of leg A or leg B, so that area A*B/2 is divisible by 3*4/2 = 6. - Lekraj Beedassy, Apr 30 2004 From Wolfdieter Lang, Jun 14 2015: (Start) This sequence gives the area/6 (in some squared length unit) of primitive Pythagorean triangles with multiplicities modulo leg exchange. See the example. This sequence also gives Fibonacci's congruous numbers divided by 24, with multiplicities and ordered nondecreasingly. See A258150. (End) It appears that this sequence gives the list of dimensions of irreducible unitary representations of the Lie group SO(5). - Antoine Bourget, Mar 30 2022 LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 Ron Knott, Pythagorean Triples and Online Calculators FORMULA a(n) = A024406(n)/6. EXAMPLE a(6) = a(7) = 35 from the two Pythagorean triangles (A,B,C) = (21, 20, 29) and (35, 12, 37) with area 210. Triangles (20, 21, 29) and (12, 35, 37) are not counted (leg exchange). - Wolfdieter Lang, Jun 14 2015 MATHEMATICA Take[Sort[(Times@@#)/12&/@({Times@@#, (Last[#]^2-First[#]^2)/2}&/@ Select[ Subsets[Range[1, 41, 2], {2}], GCD@@#==1&])], 60] (* Harvey P. Dale, Feb 27 2012 *) CROSSREFS Cf. A020882, A020883, A020884, A020886. Sequence in context: A313665 A015847 A224692 * A258151 A280320 A213365 Adjacent sequences: A020882 A020883 A020884 * A020886 A020887 A020888 KEYWORD nonn AUTHOR Clark Kimberling EXTENSIONS Extended and corrected by David W. Wilson STATUS approved

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Last modified May 23 18:13 EDT 2024. Contains 372765 sequences. (Running on oeis4.)