A025479 Largest exponents of perfect powers (A001597).

2, 2, 3, 2, 4, 2, 3, 5, 2, 2, 6, 4, 2, 2, 3, 7, 2, 2, 2, 3, 2, 5, 8, 2, 2, 3, 2, 2, 2, 2, 9, 2, 2, 4, 2, 6, 2, 2, 2, 2, 3, 10, 2, 2, 2, 4, 3, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 11, 2, 7, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 12, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 8, 2, 3, 2, 2, 2

Offset: 1

Author

David W. Wilson

Keywords

• easy
• nonn

Comments

Greatest common divisor of all prime-exponents in canonical factorization of n-th perfect power. - Reinhard Zumkeller, Oct 13 2002

Asymptotically, 100% of the terms are 2, since the density of cubes and higher powers among the squares and higher powers is 0. - Daniel Forgues, Jul 22 2014

Links

• Daniel Forgues, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A001597, A025478, A052409, A124010, A322969.

Programs

Haskell

a025479 n = a025479_list !! (n-1)  -- a025479_list is defined in A001597.
-- Reinhard Zumkeller, Mar 28 2014, Jul 15 2012

Maple

N:= 10^6: # to get terms corresponding to all perfect powers <= N
V:= Vector(N,storage=sparse);
V[1]:= 2:
for p from 2 to ilog2(N) do
  V[[seq(i^p,i=2..floor(N^(1/p)))]]:= p
od:
r,c,A := ArrayTools:-SearchArray(V):
convert(A,list); # Robert Israel, Apr 25 2017

Mathematica

Prepend[DeleteCases[#, 0], 2] &@ Table[If[Set[e, GCD @@ #[[All, -1]]] > 1, e, 0] &@ FactorInteger@ n, {n, 10^4}] (* Michael De Vlieger, Apr 25 2017 *)

PARI

print1(2,", "); for(k=2, 3^8, if(j=ispower(k),print1(j,", "))) \\ Hugo Pfoertner, Jan 01 2019

Formula

a(n) = A052409(A001597(n)). - Reinhard Zumkeller, Oct 13 2002

A001597(n) = A025478(n)^a(n). - Reinhard Zumkeller, Mar 28 2014

Extensions

Definition corrected by Daniel Forgues, Mar 07 2009