### Natural divisors and the brownian motion

A model of the Brownian motion defined in terms of the natural divisors is proposed and weak convergence of the related measures in the space $\mathbf{D}$ [0,1] is proved. An analogon of the Erdös arcsine law, known for the prime divisors [6] (see [14] for the proof), is obtained. These results together with the author’s investigation [15] extend the systematic study [9] of the distribution of natural divisors. Our approach is based upon the functional limit theorems of probability theory.