2005 AIME I Problem 12

For positive integers n, let \tau(n) denote the number of positive integer divisors of n, including 1 and n. For example, \tau(1)=1 and \tau(6)=4. Define S(n) by

$$S(n)=\tau(1)+\tau(2)+\cdots+\tau(n)$$

Let a denote the number of positive integers n \leq 2005 with S(n) odd, and let b denote the number of positive integers n \leq 2005 with S(n) even. Find |a-b|.