# Slightly odd

$\large S_n=\sum_{i=1}^n \left \lfloor{\frac{n}{i}}\right \rfloor$

$$S_n$$ is defined as of above, for all positive integers $$n$$. Determine the number of positive integers $$1<a<1616$$ for which the value of the expression

$\large S_{a-1}+S_{a}$

is an odd positive integer.

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