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A203025 Largest perfect power divisor of n.

%I A203025 #29 Jun 02 2025 14:48:40
%S A203025 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 A203025 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 A203025 64,1,1,1,4,1,1,1,36,1,1,25,4,1,1,1,16,81,1
%N A203025 Largest perfect power divisor of n.
%C A203025 This sequence shares many elements with A057521, but is not identical: A057521(72)=72 but a(72)=36.
%C A203025 Not multiplicative: a(49)=49; a(125)=125, a(49*125) = 1225 <> 49*125.
%H A203025 Giovanni Resta, <a href="/A203025/b203025.txt">Table of n, a(n) for n = 1..10000</a>
%F A203025 a(n) = max{ A001597(k) : A001597(k)|n }. - _R. J. Mathar_, Jun 09 2016
%e A203025 a(40)=a(2^3*5)=2^3=8.
%p A203025 A203025:=proc(n)
%p A203025     local a,Le,d,i,k,pe;
%p A203025     pe := ifactors(n)[2];
%p A203025     Le := {seq(i[2],i=pe)} minus {1};
%p A203025     a := 1;
%p A203025     for k in Le do
%p A203025         d := mul(i[1]^(k*floor(i[2]/k)), i=pe) ;
%p A203025         a:=max(a,d);
%p A203025     end do;
%p A203025     a
%p A203025 end proc:
%p A203025 seq(A203025(n),n=1..10000); # _Felix Huber_, Jun 01 2025
%t A203025 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 A203025 (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 A203025 Cf. A057521, A087320, A274006.
%K A203025 nonn
%O A203025 1,4
%A A203025 _Antonio Roldán_, Dec 28 2011
%E A203025 Values matching definition restored by _Franklin T. Adams-Watters_, Jun 06 2016