A111134 Numbers of the form p^(p^k-1) (p prime, k>=0).

1, 2, 8, 9, 128, 625, 6561, 32768, 117649, 2147483648, 25937424601, 2541865828329, 23298085122481, 59604644775390625, 9223372036854775808, 48661191875666868481, 104127350297911241532841, 907846434775996175406740561329, 147808829414345923316083210206383297601

Offset: 1

Author

Franz Vrabec, Oct 17 2005

Keywords

• nonn

Comments

The refactorable prime powers A000961.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..102

Crossrefs

Intersection of A000961 and A033950.

The sequence forms a subsequence of the refactorable numbers A033950; on the other hand A036878 is a subsequence.

Programs

Mathematica

f[p_, max_] := Module[{k = 1, s = {}, r}, While[(r = p^(p^k - 1)) < max, AppendTo[s, r]; k++]; s]; seq[max_] := Module[{s = {1}, p = 2, s1}, While[(s1 = f[p, max]) != {}, s = Join[s, s1]; p = NextPrime[p]]; Union[s]]; seq[10^30] (* Amiram Eldar, Aug 01 2024 *)

Extensions

More terms from Robert G. Wilson v, Oct 21 2005

a(18)-a(19) from Amiram Eldar, Aug 01 2024