Lovely Divisor

Number Theory Level pending

A positive integer x is called lovely if and only if there is no such positive integer a > 1 such that a^2 is a divisor of x. You have to find the largest possible divisor that fills this criteria

Suppose for 10 , there are divisors : 1 , 2 , 5 , 10 ... Here 10 is the highest divisor of 10 , that isn't divisible by any perfect square..

For 12 = 1 , 2 , 3 , 4 , 6 , 12 .. Here 12 is divisible by 4, that is a perfect square , 4 = 2 ^ 2 .. so the optimal answer would be 6. ( 6 is the lovely divisor )

Now for integer 123456789 , what is the largest possible lovely divisor ?

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