A072814 Smallest exponents of perfect powers: A001597(n)=A072813(n)^a(n).

2, 2, 3, 2, 2, 2, 3, 5, 2, 2, 2, 2, 2, 2, 3, 7, 2, 2, 2, 3, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 11, 2, 7, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3

Offset: 1

Author

Reinhard Zumkeller, Jul 12 2002

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Perfect Power.

Programs

Mathematica

{2}~Join~Map[Function[m, Min@ DeleteCases[#, x_ /; x < 2] &@ Table[Boole[k^# == m] # &@ IntegerExponent[m, k], {k, 2, Floor@ Sqrt@ m}]], Select[Range@ 5000, GCD @@ FactorInteger[#][[All, -1]] > 1 &]] (* Michael De Vlieger, Dec 08 2016 *)

Extensions

Definition corrected by Daniel Forgues, Mar 07 2009

Inserted a(1) = 2 by Gionata Neri, Dec 08 2016