Sur un problème de S. Ramanujan

In 1915, Srinivasa Ramanujan gives a lower limit for the maximum order of the iterated of the divisors function, d(d(n)). In 1989, Paul Erdős and Aleksandar Ivić give a upper bound. In this Note, we find the maximal order of the function ω(d(n)), the number of prime divisors of d(n), and we improve the result of Erdős and Ivić on the maximal order of d(d(n)). To cite this article: A. Smati, C. R. Acad. Sci. Paris, Ser. I 340 (2005).