A problem of Ramanujan, Erdos and Katai on the iterated divisor function
  We determine asymptotically the maximal order of log d(d(n)), where d(n) is the number of positive divisors of n. This solves a problem first put forth by Ramanujan in 1915. 
Yvonne Buttkewitz, Christian Elsholtz, Kevin Ford and Jan-Christoph   Schlage-Puchta
math.NT