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Pseudo Square Root

Problem 266

Published on Saturday, 28th November 2009, 01:00 pm; Solved by 992

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 1016.