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
Keywords
Examples
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.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000
Programs
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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 *)
Formula
{k >0: k^2 in A024975}. [R. J. Mathar, Oct 06 2009]
Extensions
Comments moved to the examples by R. J. Mathar, Oct 07 2009
Title corrected by Jeppe Stig Nielsen, Jan 26 2015