%I A052409
%S A052409 0,1,1,2,1,1,1,3,2,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,2,1,3,1,1,1,1,5,1,1,1,
%T A052409 2,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6,1,1,1,1,1,1,
%U A052409 1,1,1,1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1
%N A052409 a(n) = largest integer power m for which a representation of the form 
               n = k^m exists (for some k).
%C A052409 Greatest common divisor of all prime-exponents in canonical factorization 
               of n for n>1: a(n)>1 iff n is a perfect power; a(A001597(k))=A025479(k). 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 13 2002
%C A052409 a(1) set to 0 since there is no largest finite integer power m for which 
               a representation of the form 1 = 1^m exists (infinite largest m). 
               [From Daniel Forgues (squid(AT)zensearch.com), Mar 06 2009]
%H A052409 Daniel Forgues, <a href="b052409.txt">Table of n, a(n) for n=1..100000</
               a>
%H A052409 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Power.html">Power</a>
%H A052409 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PerfectPower.html">Perfect Power</a>
%e A052409 n=72=2.2.2.3.3: GCD[exponents]=GCD[3,2]=1. It deviates from Min of exponents(A051904).
%t A052409 Table[GCD @@ Last /@ FactorInteger[n], {n, 100}] (*Chandler*)
%Y A052409 Cf. A052410, A005361, A051903, A051904, A072411-A072414.
%Y A052409 Sequence in context: A145037 A158052 A158378 this_sequence A051904 A070012 
               A071178
%Y A052409 Adjacent sequences: A052406 A052407 A052408 this_sequence A052410 A052411 
               A052412
%K A052409 nonn
%O A052409 1,4
%A A052409 Eric Weisstein (eric(AT)weisstein.com)
%E A052409 More terms from Labos E. (labos(AT)ana.sote.hu), Jun 17 2002