Given a positive integer N. Find the largest divisor of the given number that is not divisible by a perfect square greater than 1.
Input : 12 Output : 6 Explanation : Divisors of 12 are 1, 2, 3, 4, 6 and 12. Since 12 is divisible by 4 (a perfect square), it can't be required divisor. 6 is not divisible by any perfect square. Input :97 Output :97
A simple approach is to find all the divisors of the given number N by iterating upto square root of N and keep them in sorted order(Descending) in a list. Here we are inserting them in a set in descending order to keep them sorted. Also, make a list of all perfect squares upto 1010 by iterating from 1 to 105.
Now for each divisor starting from the greatest one check whether it is divisible by any perfect square in the list or not. If a divisor is not divisible by any perfect, simply return it as the answer.
Below is the implementation of the above approach.
An efficient approach is to divide n by i for every i such that (i * i) divides n.
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