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%I #27 Jun 09 2016 05:35:14
%S 1,1,1,4,1,1,1,8,9,1,1,4,1,1,1,16,1,9,1,4,1,1,1,8,25,1,27,4,1,1,1,32,
%T 1,1,1,36,1,1,1,8,1,1,1,4,9,1,1,16,49,25,1,4,1,27,1,8,1,1,1,4,1,1,9,
%U 64,1,1,1,4,1,1,1,36,1,1,25,4,1,1,1,16,81,1
%N Largest perfect power divisor of n.
%C This sequence shares many elements with A057521, but is not identical: A057521(72)=72 but a(72)=36.
%C Not multiplicative: a(49)=49; a(125)=125, a(49*125) = 1225 <> 49*125.
%H Giovanni Resta, <a href="/A203025/b203025.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = max{ A001597(k) : A001597(k)|n }. - _R. J. Mathar_, Jun 09 2016
%e a(40)=a(2^3*5)=2^3=8.
%p A203025 := proc(n)
%p local a,d;
%p a := 1;
%p for d in numtheory[divisors](n) do
%p if isA001597(d) then # implemented in A001597
%p a := max(a,d) ;
%p end if;
%p end do:
%p return a;
%p end proc: # _R. J. Mathar_, Jun 09 2016
%t Table[If[SquareFreeQ[n], 1, s = FactorInteger[n]; Max[Table[Times @@ Cases[s, {p_, ep_} :> p^i /; (ep >= i)], {i, 2, Max[s[[All, 2]]]}]]], {n, 100}] (* _Olivier Gerard_, Jun 03 2016 *)
%o (PARI) a(n)=my(f=factor(n),mx=1);for(e=2,if(n>1,vecmax(f[,2])), mx=max(mx,prod(i=1,#f[,1],f[i,1]^(f[i,2]\e*e))));mx \\ _Charles R Greathouse IV_, Dec 28 2011
%Y Cf. A057521, A087320, A274006.
%K nonn
%O 1,4
%A _Antonio Roldán_, Dec 28 2011
%E Values matching definition restored by _Franklin T. Adams-Watters_, Jun 06 2016
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