# How to deal with the reciprocal?

Number Theory Level 3

Denote $$d_1, d_2, d_3, \ldots , d_n$$ as the distinct positive integral divisors of the number $$10500$$.

What is the range of the sum: $$\displaystyle S = \sum_{k=1}^{n} \frac 1 {d_k}$$?

Bonus: Find the exact value of $$S$$.

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