A093771 Perfect powers for which the exponent is a prime number: solutions to {A051409(x) is prime}.

4, 8, 9, 25, 27, 32, 36, 49, 100, 121, 125, 128, 144, 169, 196, 216, 225, 243, 289, 324, 343, 361, 400, 441, 484, 529, 576, 676, 784, 841, 900, 961, 1000, 1089, 1156, 1225, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936, 2025, 2048, 2116, 2187

Offset: 1

Author

Labos Elemer, Apr 19 2004

Keywords

• nonn

Comments

A010051(A025479(n)) = 1. - Reinhard Zumkeller, Mar 28 2014

Examples

			All 2-,3-,5-,7th ... powers are here, 4-,6-,8th etc. powers are excluded
from A001597.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001157, A025479, A052409, A001597.

Programs

Haskell

a093771 n = a093771_list !! (n-1)
a093771_list = [a001597 x | x <- [2..], a010051 (a025479 x) == 1]
-- Reinhard Zumkeller, Mar 28 2014

Mathematica

ffi[x_] :=Flatten[FactorInteger[x]] ep[x_] :=Table[Part[ffi[x], 2*w], {w, 1, lf[x]}] lf[x_] :=Length[FactorInteger[x]] Do[If[PrimeQ[Apply[GCD, ep[n]]], Print[n]], {n, 2, 10000}]

PARI

is(n)=isprime(ispower(n)) \\ Charles R Greathouse IV, Oct 19 2015

Formula

GCD of prime-exponents in canonical factorization of n is prime.