A078388 Arithmetic derivative of numbers which can be written as sum of a positive square and a positive cube.

1, 1, 6, 7, 16, 1, 44, 15, 32, 1, 14, 60, 1, 1, 48, 45, 56, 22, 51, 18, 72, 156, 1, 80, 176, 43, 1, 20, 140, 1, 216, 1, 63, 165, 1, 448, 46, 69, 50, 34, 152, 185, 236, 30, 168, 129, 123, 151, 62, 42, 216, 252, 1, 284, 105, 432, 38, 284, 1, 240, 115, 356, 1, 1, 211, 456

Offset: 1

Author

Reinhard Zumkeller, Nov 25 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A003415, A055394, A078386.

Programs

Mathematica

ad[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); ad /@ Select[Range[300], Length[Reduce[a^2 + b^3 == # && a > 0 && b > 0, {a, b}, Integers]] > 0 &] (* Amiram Eldar, Mar 27 2025 *)

Formula

a(n) = A003415(A055394(n)). - Amiram Eldar, Mar 27 2025