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A025479 Largest exponents of perfect powers (A001597).

%I A025479 #30 Jan 01 2019 07:01:21
%S A025479 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 A025479 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 A025479 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 A025479 Largest exponents of perfect powers (A001597).
%C A025479 Greatest common divisor of all prime-exponents in canonical factorization of n-th perfect power. - _Reinhard Zumkeller_, Oct 13 2002
%C A025479 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 A025479 Daniel Forgues, <a href="/A025479/b025479.txt">Table of n, a(n) for n=1..10000</a>
%F A025479 a(n) = A052409(A001597(n)). - _Reinhard Zumkeller_, Oct 13 2002
%F A025479 A001597(n) = A025478(n)^a(n). - _Reinhard Zumkeller_, Mar 28 2014
%p A025479 N:= 10^6: # to get terms corresponding to all perfect powers <= N
%p A025479 V:= Vector(N,storage=sparse);
%p A025479 V[1]:= 2:
%p A025479 for p from 2 to ilog2(N) do
%p A025479   V[[seq(i^p,i=2..floor(N^(1/p)))]]:= p
%p A025479 od:
%p A025479 r,c,A := ArrayTools:-SearchArray(V):
%p A025479 convert(A,list); # _Robert Israel_, Apr 25 2017
%t A025479 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 A025479 (Haskell)
%o A025479 a025479 n = a025479_list !! (n-1)  -- a025479_list is defined in A001597.
%o A025479 -- _Reinhard Zumkeller_, Mar 28 2014, Jul 15 2012
%o A025479 (PARI) print1(2,", "); for(k=2, 3^8, if(j=ispower(k),print1(j,", "))) \\ _Hugo Pfoertner_, Jan 01 2019
%Y A025479 Cf. A001597, A025478, A052409, A124010, A322969.
%K A025479 easy,nonn
%O A025479 1,1
%A A025479 _David W. Wilson_
%E A025479 Definition corrected by _Daniel Forgues_, Mar 07 2009