I seek a reference for the fact that "coefficients of the Hirzebruch $L$-polynomial have odd denominators". The coefficients are
$$\frac{2^{2k}(2^{2k-1}-1)B\_k}{(2k)!}$$ where $B\_k$ is the Bernoulli number, but I cannot locate the appropriate divisibility property of $B\_k$. Of course, $2^{2k-1}-1$ is odd, so it can be ignored. 



Coefficients in Hirzebruch polynomial and divisibility of Bernoulli numbers: reference request
This follows from the Clausen - von Staudt theorem. See <http://www.bernoulli.org> (structure of the denominator)


