A165454 Numbers the squares of which are sums of three distinct positive cubes.

6, 15, 27, 48, 53, 59, 71, 78, 84, 87, 90, 96, 98, 116, 120, 121, 125, 134, 153, 162, 163, 167, 180, 188, 204, 213, 216, 224, 225, 226, 230, 240, 242, 244, 251, 253, 255, 262, 264, 280, 287, 288, 303, 314, 324, 330, 342, 350, 356, 363, 368, 372, 381, 384, 393

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

{k >0: k^2 in A024975}. [R. J. Mathar, Oct 06 2009]

Example

6 is in the sequence because 6^2 = 1^3+2^3+3^3.
15 is in the sequence because 15^2 = 1^3+2^3+6^3.

Maple

N:= 1000: # to get all terms <= N
sc:= {seq(seq(seq(a^3 + b^3 + c^3, a = 1 .. min(b-1, floor((N^2 - b^3 - c^3)^(1/3)))), b = 2 .. min(c-1, floor((N^2 - c^3)^(1/3)))), c = 3 .. floor(N^(2/3)))}:
select(t -> member(t^2, sc), [$1..N]); # Robert Israel, Jan 27 2015

Mathematica

lst={}; Do[Do[Do[d=Sqrt[a^3+b^3+c^3]; If[d<=834&&IntegerQ[d], AppendTo[lst, d]], {c, b+1, 5!, 1}], {b, a+1, 5!, 1}], {a, 5!}]; Take[Union@lst, 123]
Sqrt[# ]&/@Select[Total/@Subsets[Range[50]^3, {3}], IntegerQ[Sqrt[#]]&]// Union (* Harvey P. Dale, Oct 14 2020 *)

Crossrefs

Cf. A161992, A024973, A025399

Sequence in context: A171972 A225285 A353603 * A333646 A063525 A335267

Adjacent sequences: A165451 A165452 A165453 * A165455 A165456 A165457

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Sep 20 2009

Extensions

Comments moved to the examples by R. J. Mathar, Oct 07 2009

Title corrected by Jeppe Stig Nielsen, Jan 26 2015

Status

approved