A025479 - OEIS

%I #30 Jan 01 2019 07:01:21

%S 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,

%T 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,

%U 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

%N Largest exponents of perfect powers (A001597).

%C Greatest common divisor of all prime-exponents in canonical factorization of n-th perfect power. - _Reinhard Zumkeller_, Oct 13 2002

%C 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

%H Daniel Forgues, <a href="/A025479/b025479.txt">Table of n, a(n) for n=1..10000</a>

%F a(n) = A052409(A001597(n)). - _Reinhard Zumkeller_, Oct 13 2002

%F A001597(n) = A025478(n)^a(n). - _Reinhard Zumkeller_, Mar 28 2014

%p N:= 10^6: # to get terms corresponding to all perfect powers <= N

%p V:= Vector(N,storage=sparse);

%p V[1]:= 2:

%p for p from 2 to ilog2(N) do

%p   V[[seq(i^p,i=2..floor(N^(1/p)))]]:= p

%p od:

%p r,c,A := ArrayTools:-SearchArray(V):

%p convert(A,list); # _Robert Israel_, Apr 25 2017

%t 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 *)

%o (Haskell)

%o a025479 n = a025479_list !! (n-1)  -- a025479_list is defined in A001597.

%o -- _Reinhard Zumkeller_, Mar 28 2014, Jul 15 2012

%o (PARI) print1(2,", "); for(k=2, 3^8, if(j=ispower(k),print1(j,", "))) \\ _Hugo Pfoertner_, Jan 01 2019

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

%K easy,nonn

%O 1,1

%A _David W. Wilson_

%E Definition corrected by _Daniel Forgues_, Mar 07 2009