On the iteration of the number of divisors without large prime factors
Let \(d(n)\) denote the number of divisors of \(n\) and \(d(d(n))\) be the iterated divisor function. Among others \textit{E. Heppner} [J. Reine Angew. Math. 265, 176-182 (1974; Zbl 0273.10037)] proved an asymptotic representation for the sum \(\sum_{n\leq x} d(d(n))\). The author considers the same sum, but under the restriction \(p(n)\leq y\leq x\), where \(p(n)\) denotes the greatest prime divisor of \(n\). Further, asymptotic results are given for the sum \[ \sum_{n\leq x} {d(d(n))\over p(n)} \] and similar sums.
scientific article; zbMATH DE number 874230