

A136360


Square roots of the perfect squares in A133459.


2



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
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OFFSET

1,1


COMMENTS

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, ...}.


LINKS

Table of n, a(n) for n=1..52.


FORMULA

a(n) = Sqrt[ A136359(n) ].


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A136359, A136361, A133459, A002311, A002411, A053721.
Sequence in context: A001474 A084806 A020938 * A023483 A023042 A128245
Adjacent sequences: A136357 A136358 A136359 * A136361 A136362 A136363


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Dec 25 2007


STATUS

approved



