Erdős problem 289

Is it true that, for all sufficiently large $k$, there exists finite intervals $I_1, \dotsc, I_k \subset \mathbb{N}$ with $|I_i| \geq 2$ for $1 \leq i \leq k$ such that $$1 = \sum_{i=1}^k \sum_{n \in I_i} \frac{1}{n}.$$