A078360 Numbers having a unique representation as sum of a positive square and a positive cube.

2, 5, 9, 10, 12, 24, 26, 28, 31, 33, 36, 37, 43, 44, 50, 52, 57, 63, 68, 72, 73, 76, 80, 82, 91, 100, 101, 113, 122, 126, 127, 128, 134, 141, 148, 150, 152, 161, 164, 170, 171, 174, 177, 185, 189, 196, 197, 204, 206, 208, 217, 220, 223, 226, 232, 241, 246, 257

Offset: 1

Author

Reinhard Zumkeller, Nov 25 2002

Keywords

• nonn

Examples

			10 is a term, as 10 = 3^2 + 1^3 and all other sums of positive squares and positives cubes are not equal 10.
17 is not a term, as 17 = 3^2 + 2^3 = 4^2 + 1^3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055394, A054402, A078359.

Programs

Mathematica

Select[Range[300], Length[Solve[a^2 + b^3 == # && a > 0 && b > 0, {a, b}, Integers]] == 1 &] (* Amiram Eldar, Mar 27 2025 *)

Formula

A078359(a(n))=1.