A136360 - OEIS

%I #7 Jun 06 2021 20:39:44

%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.

%C Note that some numbers in a(n) are also perfect squares: m = k^2 = {9, 25, 961, 17424, ...}. The corresponding numbers k such that a(n) = k^2 are listed in A136361.

%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