A076292 - OEIS

%I #13 Jan 01 2022 09:56:28

%S 1,4,8,9,16,25,27,32,36,49,64,81,100,121,125,128,169,196,216,225,243,

%T 256,289,343,361,441,484,512,529,625,676,729,841,900,961,1000,1024,

%U 1089,1156,1225,1296,1331,1369,1444,1521,1681,1764,1849,2048,2116,2187

%N Perfect powers with squarefree root.

%H Amiram Eldar, <a href="/A076292/b076292.txt">Table of n, a(n) for n = 1..10000</a>

%F A025478(a(n)) = A007947(a(n)).

%e A001597(17) = 144 = (3*2^2)^2 is not a term.

%t q[n_] := n == 1 || Length[(u = Union[FactorInteger[n][[;;,2]]])] == 1 && u[[1]] > 1; Select[Range[2000], q] (* _Amiram Eldar_, Jan 01 2022 *)

%o (PARI) is(n)=n==1 || (ispower(n,,&n) && issquarefree(n)) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A001597, A025478, A005117, A007947, A072777.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Nov 06 2002