# The sum of reciprocals of odd numbers

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.

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Found by hand in under 2 minutes: $1/3 + 1/5 + 1/7 + 1/9 + 1/15 + 1/21 + 1/23 + 1/35 + 1/63 + 1/105 + 1/1035 = 1$ – Woett Apr 8 '12 at 21:20

In fact, you can choose the $n_i$ so that the sum is $1$: see the discussion at http://www.ics.uci.edu/~eppstein/numth/egypt/odd-one.html