J. Integer Seq. 6(2), Art. 03.2.7, 7 p., electronic only (2003)
Summary
Summary: In 2003 Cohen and Iannucci introduced a multiplicative arithmetic function $D$ by assigning $D(p^a) = a$ p^a-1 when $p$ is a prime and $a$ is a positive integer. They defined D^$0(n) = n$ and $D^k(n) = $D(D^k-1$(n))$ and they called $(D^k(n))$, k >= 0 the derived sequence of $n$. This paper answers some open questions about the function $D$ and its iterates. We show how to construct derived sequences of arbitrary cycle size, and we give examples for cycles of lengths up to 10. Given $n$, we give a method for computing $m$ such that $D(m)=n$, up to a square free unitary factor.
