  We consider the set of finite sequences of length n over a finite or
countable alphabet C. We consider the function which associate each given
sequence with the size of the maximum overlap with a (shifted) copy of itself.
We compute the exact distribution and the limiting distribution of this
function when the sequence is chosen according to a product measure with
marginals identically distributed. We give a point-wise upper bound for the
velocity of this convergence. Our results holds for a finite or countable
alphabet. The non-parametric distribution is related to the prime decomposition
of positive integers. We illustrate with some examples.
