I have a question that I've been thinking for a while now.

*Can you find a set of distinct positive odd integers* $n_1, n_2, \ldots, n_k$ *for some finite positive integer* $k$ *such that* $\left(\frac{1}{n_1} + \frac{1}{n_2} + \ldots + \frac{1}{n_k} \right)$ *is a positive integer as well?*

This statement obviously holds if we allow $n_1 \ldots n_k$ to be even. I'd be glad if you can recommend some articles that study this particular problem.