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%I #18 Aug 09 2019 01:55:23
%S 1,2,4,3,6,4,9,8,12,5,10,16,15,6,12,20,18,7,25,24,14,21,30,8,28,16,36,
%T 24,35,32,9,18,42,40,27,36,49,48,10,20,45,30,56,40,54,11,22,50,64,33,
%U 63,60,44,12,72,55,24,70,36,66,48,81,80,60,13,77,26,39
%N Areas of integer rectangles circumscribed by increasingly large circles.
%C Sort all rectangles with integer side lengths by the radius of the circle that circumscribes them. Ties are broken by sorting by area. The terms of the sequence are the areas of the rectangles.
%e a(1) is a 1 X 1 rectangle; r = sqrt(1^2 + 1^2) = sqrt(2); A = 1.
%e a(2) is a 2 X 1 rectangle; r = sqrt(2^2 + 1^2) = sqrt(5); A = 2.
%t Times @@@ Take[Flatten[ SortBy[#, Times @@ # &] & /@ GatherBy[ SortBy[ Union[Sort /@ Tuples[ Range[70], 2]], Total[#^2] &], Total[#^2] &], 1], 70] (* _Giovanni Resta_, Jul 18 2019 *)
%Y Cf. A024509.
%K nonn
%O 1,2
%A _Dave Rutt_, Jul 04 2019
%E More terms from _Giovanni Resta_, Jul 17 2019
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