A112474 Squares that are the sum of three distinct positive cubes.

36, 225, 729, 2304, 2809, 3481, 5041, 6084, 7056, 7569, 8100, 9216, 9604, 13456, 14400, 14641, 15625, 17956, 23409, 26244, 26569, 27889, 32400, 35344, 41616, 45369, 46656, 50176, 50625, 51076, 52900, 57600, 58564, 59536, 63001, 64009

Offset: 1

Author

Rick L. Shepherd, Sep 06 2005

Keywords

• nonn

Examples

			36 = 6^2 = 1^3 + 2^3 + 3^3.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A000290 and A024975.

Programs

Mathematica

Lim=64009;sqlim=Floor[Sqrt[Lim]];cblim=Ceiling[Lim^(1/3)]; Select[Range[sqlim]^2,MemberQ[ Union[Total/@Subsets[Range[cblim]^3,{3}]],#]&] (* James C. McMahon, Jun 04 2024 *)

PARI

has(n)=my(x3,z); for(x=sqrtnint(n\3,3)+1, sqrtnint(n,3), x3=x^3; for(y=sqrtnint((n-x3)\2,3)+1, min(x-1,sqrtnint(n-x3,3)), if(ispower(n-x3-y^3,3,&z) && z0, return(1)))); 0
list(lim)=my(v=List(),t); for(n=6,sqrtint(lim\1), if(has(t=n^2), listput(v,t))); Vec(v) \\ Charles R Greathouse IV, Sep 20 2016

Extensions

Offset corrected by Charles R Greathouse IV, Sep 20 2016