I seek a reference for the fact that "coefficients of the Hirzebruch $L$polynomial have odd denominators". The coefficients are $$\frac{2^{2k}(2^{2k1}1)B_k}{(2k)!}$$ where $B_k$ is the Bernoulli number, but I cannot locate the appropriate divisibility property of $B_k$. Of course, $2^{2k1}1$ is odd, so it can be ignored.
This follows from the clausen  Von staudt theorem. See http://www.bernoulli.orG ( structure of the denominator) 

