In the note under review the author studies the rational numbers
where are the classical famous Bernoulli numbers. He shows that these modified Bernoulli numbers have some very interesting properties similar to the classical ones, namely
a) The value of for odd is periodic mod 12;
b) The fractional part of for even is given by ;
c) , , even, where denotes the th Bessel function of the second kind.
The proofs are really fun, as the author points out, and are examples of his virtuos handling of generating functions.