A078360 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

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

FORMULA

A078359(a(n))=1.

EXAMPLE

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.

MATHEMATICA

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