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

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, 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, 1, 1, 1, 4, 1, 1, 1, 9, 1, 1, 25, 4, 1, 1, 1, 16, 81, 1

Offset: 1

Author

Franklin T. Adams-Watters, Jun 06 2016

Keywords

• nonn

Comments

These values were mistakenly entered into A203025.

Examples

			36 = 2^2 * 3^2. 3^2 = 9 > 2^2 = 4, so a(36) = 9.
20 = 2^2 * 5, so 2^2 = 4 is the only proper prime power divisor of 20, thus a(20) = 4.
		

Links

• Franklin T. Adams-Watters, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A203025, A246547.

Programs

Maple

A274006:=proc(n)
    local a, pe;
    a := 1;
    for pe in ifactors(n)[2] do
        if pe[2] > 1 then
            a:=max(a, pe[1]^pe[2]);
        end if;
    end do;
    a
end proc:
seq(A274006(n), n=1..100); # R. J. Mathar, Jun 02 2025

Mathematica

Table[s = Select[FactorInteger[n], #[[2]] > 1 &]; If[s == {}, 1, Max[#1^#2 & @@@ s]], {n, 100}] (* T. D. Noe, Jan 02 2012 *)
Table[If[SquareFreeQ[n],1,Max[#[[1]]^#[[2]]&/@Select[FactorInteger[n],#[[2]]>1&]]],{n,90}] (* Harvey P. Dale, Feb 18 2025 *)

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