# Parity of the Sums of the Number of Divisors

Number Theory Level 4

Define $$\tau(n)$$ to be the number of positive divisors of $$n$$. Let $$S_n=\tau(1)+\tau(2)+ \dots+\tau(n)$$. For how many $$n \leq 2008$$ is $$S_n$$ odd?

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