A problem of Ramanujan, Erdos and Katai on the iterated divisor function

TL;DR

This paper determines the asymptotic maximum of the iterated divisor function log d(d(n)), solving a problem posed by Ramanujan in 1915.

Contribution

It provides the first asymptotic solution to the longstanding problem of the maximal order of the iterated divisor function.

Findings

Asymptotic formula for max log d(d(n))

Resolution of Ramanujan's 1915 problem

Advancement in understanding divisor functions

Abstract

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.