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On harmonic number

Posted: Sun Jul 24, 2016 4:50 pm
by Tolaso J Kos
Let $\mathcal{H}_n$ denote the $n$-th harmonic number. Note that:

$$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{6} \in \mathbb{N}$$

Can you determine a way of creating finite subsequences of $\mathcal{H}_n$ such that the sum of each of them is a natural number?