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%I #19 Feb 28 2019 16:00:14
%S 4,6,8,10,12,12,14,16,16,18,20,20,22,24,24,24,26,28,28,30,30,32,32,34,
%T 36,36,36,38,40,40,40,42,42,44,44,46,48,48,48,48,50,52,52,54,54,56,56,
%U 56,58,60,60,60,60,62,64,64,64,66,66,68,68,70,70,72
%N For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both positive squares; list all such pairs (x,y) ordered by values of y; sequence gives y values.
%C Each even integer y >= 4 occurs A056924(y/2) times. - _Robert Israel_, Dec 10 2017
%D Donald D. Spencer, Computers in Number Theory, Computer Science Press, Rockville MD, 1982, pp. 130-131.
%H Robert Israel, <a href="/A061408/b061408.txt">Table of n, a(n) for n = 0..10000</a>
%F The solutions are given by x = r^2 + 2*r*k + 2*k^2, y = 2*k*(k+r) with r >= 1, k >= 1. - _N. J. A. Sloane_, May 02 2001
%e Pairs are [5, 4], [10, 6], [17, 8], [26, 10], [13, 12], [37, 12], [50, 14], ... For example, 5-4 = 1^2, 5+4 = 3^2.
%p seq(y $ nops(select(t -> (t^2 < y/2), numtheory:-divisors(y/2))), y=2..100,2); # _Robert Israel_, Dec 10 2017
%t Table[Table[y, {Select[Divisors[y/2], #^2 < y/2&] // Length}], {y, 2, 100, 2}] // Flatten (* _Jean-François Alcover_, Feb 28 2019, after _Robert Israel_ *)
%Y Cf. A056924, A061409, A060829, A060830.
%K nonn
%O 0,1
%A _Jason Earls_, May 01 2001
%E Definition clarified by _Robert Israel_, Dec 10 2017
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