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%I #10 Jan 10 2017 05:01:59
%S 6,39,60,210,210,410,630,915,1320,1780,2340,990,2730,3164,4620,5215,
%T 5610,4290,8145,8106,2730,6630,12116,12540,4080,17485,17451,18480,
%U 9690,24414
%N a(n) gives one fourth of the even leg of one of the two Pythagorean triangles with hypotenuse A080109(n) = A002144(n)^2. The odd leg is given in A253802(n).
%C See A253802 for comments and the Dickson reference.
%D L. E. Dickson, History of the Theory of Numbers, Carnegie Institution, Publ. No. 256, Vol. II, Washington D.C., 1920, p. 227.
%F a(n) = sqrt(A080109(n)^2 - A253802(n)^2)/4, n >= 1.
%e n = 7: A080175(7) = 7890481 = 53^4 = 2809^2; A002144(7)^4 = A253802(7)^2 + (4*a(7))^2 = 1241^2 + (4*630)^2.
%e The other Pythagorean triangle with hypotenuse
%e 53^2 = 2809 has odd leg A253804(7) = 2385 and even leg 4*A253305(7) = 4*371 = 1484: 53^4 = 2385^2 + (4*371)^2.
%Y Cf. A002144, A080109, A253802, A253804, A253805.
%K nonn,easy
%O 1,1
%A _Wolfdieter Lang_, Jan 14 2015
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