Parity of the Sums of the Number of Divisors

Define τ(n)\tau(n) to be the number of positive divisors of nn. Let Sn=τ(1)+τ(2)++τ(n)S_n=\tau(1)+\tau(2)+ \dots+\tau(n). For how many n2008n \leq 2008 is SnS_n odd?

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