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A203025 Largest perfect power divisor of n. 2
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 (list; graph; refs; listen; history; text; internal format)
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, d;

    a := 1;

    for d in numtheory[divisors](n) do

        if isA001597(d) then # implemented in A001597

            a := max(a, d) ;

        end if;

    end do:

    return a;

end proc: # R. J. Mathar, Jun 09 2016

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: A088440 A212173 A274006 * A057521 A084885 A112538

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

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Last modified July 25 06:42 EDT 2017. Contains 289779 sequences.