A078380 Maximum exponent in prime factorization of numbers which can be written as sum of a positive square and a positive cube.

1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 1, 2, 3, 1, 2, 4, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 7, 1, 1, 1, 1, 2, 2, 3, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 3, 2, 6, 1, 2, 2, 1, 3, 1, 2, 3, 5, 1, 1, 3, 1, 4, 2, 1, 1, 1, 2, 3, 1, 1, 3, 2, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Nov 25 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A051903, A055394, A078377, A078379.

Programs

Mathematica

Max[FactorInteger[#][[;; , 2]]] & /@ 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) = A051903(A055394(n)).