## Pseudo Square Root

### Problem 266

Published on Saturday, 28th November 2009, 01:00 pm; Solved by 1088; Difficulty rating: 65%
The divisors of 12 are: 1,2,3,4,6 and 12.

The largest divisor of 12 that does not exceed the square root of 12 is 3.

We shall call the largest divisor of an integer `n` that does not exceed the square root of `n` the pseudo square root (PSR) of `n`.

It can be seen that PSR(3102)=47.

Let `p` be the product of the primes below 190.

Find PSR(`p`) mod 10^{16}.