A203025 Largest perfect power divisor of n.

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, 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, 64, 1, 1, 1, 4, 1, 1, 1, 36, 1, 1, 25, 4, 1, 1, 1, 16, 81, 1

Offset

1,4

Comments

This sequence shares many elements with A057521, but is not identical: A057521(72)=72 but a(72)=36.

Not multiplicative: a(49)=49; a(125)=125, a(49*125) = 1225 <> 49*125.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

a(n) = max{ A001597(k) : A001597(k)|n }. - R. J. Mathar, Jun 09 2016

Example

a(40)=a(2^3*5)=2^3=8.

Maple

A203025:=proc(n)
    local a, Le, d, i, k, pe;
    pe := ifactors(n)[2];
    Le := {seq(i[2], i=pe)} minus {1};
    a := 1;
    for k in Le do
        d := mul(i[1]^(k*floor(i[2]/k)), i=pe) ;
        a:=max(a, d);
    end do;
    a
end proc:
seq(A203025(n), n=1..10000); # Felix Huber, Jun 01 2025

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A057521, A087320, A274006.

Sequence in context: A382906 A366993 A274006 * A057521 A393292 A387716

Adjacent sequences: A203022 A203023 A203024 * A203026 A203027 A203028

Keyword

nonn

Author

Antonio Roldán, Dec 28 2011

Extensions

Values matching definition restored by Franklin T. Adams-Watters, Jun 06 2016

Status

approved