A384419 Exponentially squarefree prime powers.

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 128, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223

Offset: 1

Author

Amiram Eldar, May 28 2025

Keywords

• nonn
• easy

Comments

Differs from A283262 by having the terms 1, 128, 1024, 2187, 8192, ..., and not having the terms 256, 512, 6561, ... .

1 and numbers of the form p^e where p is prime and e is a squarefree number.

Links

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

Crossrefs

Intersection of A000961 and A209061.

Disjoint union of {1}, A000040 and A383211.

Cf. A005117, A283262.

Programs

Mathematica

seq[lim_] := Module[{s = Select[Range[lim], !CompositeQ[#] &]}, Do[If[SquareFreeQ[i], s = Join[s, Select[Range[Surd[lim, i]], PrimeQ]^i]], {i, 2, Floor[Log2[lim]]}]; Sort[s]]; seq[250]