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

1,4

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.

Links

Table of n, a(n) for n=1..65.

Example

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.

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 *)

Crossrefs

Cf. A022549, A022550.

Sequence in context: A317625 A308447 A350506 * A351701 A099402 A248387

Adjacent sequences: A123288 A123289 A123290 * A123292 A123293 A123294

Keyword

nonn

Author

Zak Seidov, Oct 11 2006

Status

approved