A380523 Positive cubes k such that there are no primes between k and the nearest square that is not k.

8, 27, 125, 32768, 79507, 97336

Offset: 1

Author

Zhining Yang, Jan 26 2025

Keywords

• nonn
• hard
• more

Comments

There are no other terms < 2*10^30.

Examples

			125 is a term because it is a cube and there are no primes between 125 and 121, its nearest square.
		

Crossrefs

Cf. A053706, A380521, A380522, A380405.

Programs

Mathematica

b[n_] := If[IntegerQ@Sqrt@n, 0, p = NextPrime[n^3];
  If[Ceiling[Sqrt[NextPrime[p, -1]]]^2 >= p, 0, n^3]];
Select[Array[b@# &, 1000], # > 0 &]