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A203025
Largest perfect power divisor of n.
8
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
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
KEYWORD
nonn
AUTHOR
Antonio Roldán, Dec 28 2011
EXTENSIONS
Values matching definition restored by Franklin T. Adams-Watters, Jun 06 2016
STATUS
approved