A076403 Squarefree kernel of n-th perfect power.

1, 2, 2, 3, 2, 5, 3, 2, 6, 7, 2, 3, 10, 11, 5, 2, 6, 13, 14, 6, 15, 3, 2, 17, 6, 7, 19, 10, 21, 22, 2, 23, 6, 5, 26, 3, 14, 29, 30, 31, 10, 2, 33, 34, 35, 6, 11, 37, 38, 39, 10, 41, 6, 42, 43, 22, 15, 2, 46, 3, 13, 47, 6, 7, 10, 51, 26, 14, 53, 6, 55, 5, 14, 57, 58, 15, 59, 30, 61, 62

Offset: 1

Author

Reinhard Zumkeller, Oct 09 2002

Keywords

• nonn

Comments

a(n) = A007947(A001597(n)).

Links

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

Crossrefs

Cf. A025478.

Programs

Haskell

a076403 = a007947 . a025478 -- Reinhard Zumkeller, Mar 28 2014

Mathematica

Prepend[Map[Times @@ FactorInteger[#][[All, 1]] &, DeleteCases[#, 0]], 1] &@ Table[If[Set[e, GCD @@ #[[All, -1]]] > 1, Power[n, 1/e], 0] &@ FactorInteger[n], {n, 4000}] (* Michael De Vlieger, Apr 25 2017 *)

Formula

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