Thought Process

I started by brute forcing the first 1,000 values and a very clear pattern can be seen (And it continued for first 10,000)

• P(1,10^3) = 499 = floor(998/1) - floor(998/lcm(1,2))

• P(2,10^3) = 333 = floor(998/lcm(1,2)) - floor(998/lcm(1,2,3))

• P(3,10^3) = 83 = floor(998/lcm(1,2,3)) - floor(998/lcm(1,2,3,4))

• P(4,10^3) = 67 = floor(998/lcm(1,2,3,4)) - floor(998/lcm(1,2,3,4,5))

• P(5,10^3) = 0 = floor(998/lcm(1,2,3,4,5)) - floor(998/lcm(1,2,3,4,5,6))

Once I realised this, all that was left was to prove it was true, and it is quite clear using the Chinese Remainder Theorem

From this I can deduce that P(a,b) = floor((b-2)/lcm(1,2,...,a)) - floor((b-2)/lcm(1,2,...,a,a+1))

I added an LCM function to my Essential Functions page