A136360 Square roots of the perfect squares in A133459.

6, 9, 12, 17, 22, 24, 25, 26, 60, 86, 99, 120, 188, 200, 202, 210, 214, 238, 243, 268, 336, 348, 415, 476, 481, 504, 524, 539, 565, 602, 693, 704, 720, 726, 732, 846, 899, 961, 965, 990, 1026, 1202, 1218, 1221, 1224, 1320, 1551, 1602, 1687, 1716, 1724, 1734

Offset: 1

Author

Alexander Adamchuk, Dec 25 2007

Keywords

• nonn

Comments

Corresponding squares in A133459 are listed in A136359(n) = a(n)^2.

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.

Examples

			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, ...}.
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.
		

Crossrefs

Cf. A136359, A136361, A133459, A002311, A002411, A053721.

Programs

Mathematica

Sqrt[ Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i,1,300}, {j,1,i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ] ]

Formula

a(n) = sqrt(A136359(n)).