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
Keywords
Links
- Eric Weisstein's World of Mathematics, Perfect Power.
Programs
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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