%I
%S 6,9,12,17,22,24,25,26,60,86,99,120,188,200,202,210,214,238,243,268,
%T 336,348,415,476,481,504,524,539,565,602,693,704,720,726,732,846,899,
%U 961,965,990,1026,1202,1218,1221,1224,1320,1551,1602,1687,1716,1724,1734
%N Square roots of the perfect squares in A133459.
%C Corresponding squares in A133459 are listed in A136359(n) = a(n)^2 = {36,81,144,289,484,576,625,676,3600,...}. Note that some numbers in a(n) are also the perfect squares: m = k^2 = {9, 25, 961, 17424, ...}. The corresponding numbers k such that a(n) = k^2 are listed in A136361 = {3, 5, 31, 132, ...}.
%F a(n) = Sqrt[ A136359(n) ].
%e A133459 begins {2,7,12,19,24,36,41,46,58,76,80,81,93,115,127,132,144,150,166,197,201,202,214,236,252,271,289,...}.
%e Thus a(1) = Sqrt[36] = 6, a(2) = Sqrt[81] = 9, a(3) = Sqrt[144] = 12, a(4) = Sqrt[289] = 17 that are the square roots of the perfect squares in A133459.
%t Sqrt[ Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i,1,300}, {j,1,i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ] ]
%Y Cf. A136359, A136361, A133459, A002311, A002411, A053721.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Dec 25 2007
