cp's OEIS Frontend

A274006 Largest proper prime power divisor of n, or 1 if n is squarefree.

%I A274006 #14 Jun 03 2025 07:28:43
%S A274006 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 A274006 1,1,1,9,1,1,1,8,1,1,1,4,9,1,1,16,49,25,1,4,1,27,1,8,1,1,1,4,1,1,9,64,
%U A274006 1,1,1,4,1,1,1,9,1,1,25,4,1,1,1,16,81,1
%N A274006 Largest proper prime power divisor of n, or 1 if n is squarefree.
%C A274006 These values were mistakenly entered into A203025.
%H A274006 Franklin T. Adams-Watters, <a href="/A274006/b274006.txt">Table of n, a(n) for n = 1..10000</a>
%e A274006 36 = 2^2 * 3^2. 3^2 = 9 > 2^2 = 4, so a(36) = 9.
%e A274006 20 = 2^2 * 5, so 2^2 = 4 is the only proper prime power divisor of 20, thus a(20) = 4.
%p A274006 A274006:=proc(n)
%p A274006     local a, pe;
%p A274006     a := 1;
%p A274006     for pe in ifactors(n)[2] do
%p A274006         if pe[2] > 1 then
%p A274006             a:=max(a, pe[1]^pe[2]);
%p A274006         end if;
%p A274006     end do;
%p A274006     a
%p A274006 end proc:
%p A274006 seq(A274006(n), n=1..100); # _R. J. Mathar_, Jun 02 2025
%t A274006 Table[s = Select[FactorInteger[n], #[[2]] > 1 &]; If[s == {}, 1, Max[#1^#2 & @@@ s]], {n, 100}] (* _T. D. Noe_, Jan 02 2012 *)
%t A274006 Table[If[SquareFreeQ[n],1,Max[#[[1]]^#[[2]]&/@Select[FactorInteger[n],#[[2]]>1&]]],{n,90}] (* _Harvey P. Dale_, Feb 18 2025 *)
%o A274006 (PARI) a(n) = my(fm=factor(n),r=1); for(k=1, #fm[,1], if(fm[k,2]!=1&&fm[k,1]^fm[k,2]>r, r=fm[k,1]^fm[k,2]));r
%Y A274006 Cf. A203025, A246547.
%K A274006 nonn
%O A274006 1,4
%A A274006 _Franklin T. Adams-Watters_, Jun 06 2016