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A203025
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Largest perfect power divisor of n.
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8
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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
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OFFSET
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1,4
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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a(40)=a(2^3*5)=2^3=8.
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MAPLE
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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;
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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