A123291 Numbers that are sum of a square and a nonnegative cube (with repetition).

0, 1, 1, 2, 4, 5, 8, 9, 9, 10, 12, 16, 17, 17, 24, 25, 26, 27, 28, 31, 33, 36, 36, 37, 43, 44, 49, 50, 52, 57, 63, 64, 64, 65, 65, 68, 72, 73, 76, 80, 81, 82, 89, 89, 91, 100, 100, 101, 108, 108, 113, 121, 122, 125, 126, 127, 128, 129, 129, 134, 141, 144, 145, 145, 148

Offset: 1

Author

Zak Seidov, Oct 11 2006

Keywords

• nonn

Comments

Cf. A022549 Sum of a square and a nonnegative cube (without repetition), A022550 Numbers that are not the sum of a square and a nonnegative cube.

Examples

			Each of 1, 9, 17, 36 appear two times because
1=0^2+1^3=1^2+0^3, 9=1^2+2^3=3^2+0^3, 17=3^2+2^3==4^2+1^3, 36=3^2+3^3==6^2+0^3;
225 appears three times because 225=3^2+6^3=10^2+5^3=15^2+0^3;
1025 appears four times because 1025=5^2+10^3=30^2+5^3=31^2+4^3=32^2+1^3, etc.
		

Crossrefs

Cf. A022549, A022550.

Programs

Mathematica

Lim=148; s=Ceiling[Sqrt[Lim]];c=Ceiling[Lim^(1/3)];sq=Range[0,s]^2;cb=Range[0,c]^3;seq={};Do[AppendTo[seq,sq[[i]]+cb[[j]]],{i,s+1},{j,c+1}];Sort[Select[seq,#<=Lim&]] (* James C. McMahon, Nov 19 2024 *)