A076397 Largest prime factor of n-th perfect power.

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

Offset: 1

Author

Reinhard Zumkeller, Oct 09 2002

Keywords

• nonn

Comments

a(n) = A006530(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, Greatest Prime Factor.

Crossrefs

Cf. A025478, A076396, A076403.

Programs

Haskell

a076397 = a006530 . a025478 -- Reinhard Zumkeller, Mar 28 2014

Mathematica

perfPQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1; Join[ {1},FactorInteger[ #][[-1,1]]&/@ Select[Range[5000],perfPQ]] (* Harvey P. Dale, Sep 12 2021 *)

Formula

a(n) = A006530(A025478(n)).