[math-fun] Reference for: sum of 1/(2k - 1) is not an integer

In a paper I'm working on, I want to claim that for n > 1, Sum[1/(1k - 1), {k, 1, n}] is not an integer. The result is peripheral to what the paper is about, so I hesitate to spend space proving it there. I'd like to just cite a source for the claim. Can anyone give a reference to where this claim is proved? Thanks, Bob