Is there a built-in function in Mathematica for the greatest square-free divisor of an integer (which I believe is also called the radical or square-free kernel of an integer). I know I can write my own function, but it seems to me there should be a built-in function.
I searched around a bit and I couldn’t find anything aside from truth statements. I’m no expert in mathematica though, but it doesn’t seem like there’s a built in function.
It will help always to give an example of the input and the expected output of the function you are looking for, or at give a link to an example.
But why can’t you use combination of SquareFreeQ and FactorInteger and Max?
I’m not aware of any such. Probably best to do the “obvious” thing: factor and clip powers to unity.
squareFreePart[n_Integer] := Times @@ FactorInteger[n][[All, 1]]
squareFreePart[111111111]
(* Out[491]= 37037037 *)
squareFreePart[Times @@ (Range[10]^Range[10])]
(* Out[493]= 210 *)