+33 Find the number of fractions less than 1 such that, in lowest terms, the denominator is 1000.
This is the "closed form" of the sequence that will generate all 400 numerators in the question:
a(n) = 1/4 (10 n + (1 - i) (-i)^n + (1 + i) i^n + (-1)^(n + 1) - 5)
Basically, the 400 numbers are ALL the odd numbers between 1 and 1000 of which there are 500 such numbers, exluding 100 numbers that end in 5.
