A076396 Smallest prime factor of n-th perfect power.

1, 2, 2, 3, 2, 5, 3, 2, 2, 7, 2, 3, 2, 11, 5, 2, 2, 13, 2, 2, 3, 3, 2, 17, 2, 7, 19, 2, 3, 2, 2, 23, 2, 5, 2, 3, 2, 29, 2, 31, 2, 2, 3, 2, 5, 2, 11, 37, 2, 3, 2, 41, 2, 2, 43, 2, 3, 2, 2, 3, 13, 47, 2, 7, 2, 3, 2, 2, 53, 2, 5, 5, 2, 3, 2, 3, 59, 2, 61, 2, 3, 2, 5, 2, 67, 2, 3, 2, 17, 71, 2, 73, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Oct 09 2002

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Least Prime Factor.
• Eric Weisstein's World of Mathematics, Perfect Powers.

Crossrefs

Cf. A001597, A020639, A025478, A076397, A076403.

Programs

Haskell

a076396 = a020639 . a025478 -- Reinhard Zumkeller, Mar 28 2014

Mathematica

s[n_] := If[n == 1, 1, Module[{f = FactorInteger[n]}, If[GCD @@ f[[;;, 2]] > 1, f[[1, 1]], Nothing]]]; Array[s, 10000] (* Amiram Eldar, May 16 2025 *)

Formula

a(n) = A020639(A001597(n)).

a(n) = A020639(A025478(n)).