For how many integer values of i, 1 ≤ i ≤ 1000, does there exist an integer j, 1 ≤ j ≤ 1000, such that i is a divisor of 2 ^j − 1?

is a prime number for n = odd .

In the range [1, 1000], there are 1000 numbers out of which 500 are even and 500 are odd.

So, for all odd values of i,  is divisible by i.

Thus, the number of values are 500.