Let $f (k)$ be the maximal value of $n_{1}$ such that there exist $n_{1} < n_{2} < \dots < n_{k}$ with $1 = \frac{1}{n _{1}} + \dots + \frac{1}{n _{k}} .$ Is it true that $f (k) = (1 + o (1)) \frac{k}{e - 1} ?$

Worked, still open.

number theory · solved · possible · 0 attempts

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