A076292 Perfect powers with squarefree root.

1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121, 125, 128, 169, 196, 216, 225, 243, 256, 289, 343, 361, 441, 484, 512, 529, 625, 676, 729, 841, 900, 961, 1000, 1024, 1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1681, 1764, 1849, 2048, 2116, 2187

Offset: 1

Author

Reinhard Zumkeller, Nov 06 2002

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

is(n)=n==1 || (ispower(n,,&n) && issquarefree(n)) \\ Charles R Greathouse IV, Oct 16 2015

Formula

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