A082950 Power base and exponent of n-th prime power exchanged.

0, 1, 1, 4, 1, 1, 9, 8, 1, 1, 16, 1, 1, 1, 32, 27, 1, 1, 25, 1, 1, 1, 1, 128, 1, 1, 1, 36, 1, 1, 1, 1, 64, 1, 1, 1, 1, 1, 1, 1, 1, 2048, 243, 1, 49, 1, 1, 1, 1, 1, 1, 1, 1, 8192, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 125, 1, 64, 1, 1, 1, 1, 1, 1, 1, 131072, 1, 1, 1, 1, 1, 1, 1, 2187, 1, 1, 1, 1

Offset: 1

Author

Reinhard Zumkeller, May 26 2003

Keywords

• nonn

Crossrefs

Cf. A000961, A025473, A025474.

Programs

Mathematica

s[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 1, f[[1, 2]]^f[[1, 1]], Nothing]]; s[1] = 0; Array[s, 250] (* Amiram Eldar, May 16 2025 *)

Formula

a(n) = A025474(n)^A025473(n) while A025473(n)^A025474(n) = A000961(n).

a(n) = 1 iff A000961(n) is prime.

Extensions

a(71) and following corrected by Georg Fischer, Dec 09 2022