an:02000845
Zbl 1058.11080
Hare, Kevin G.; Yazdani, Soroosh
Further results on derived sequences
EN
J. Integer Seq. 6, No. 2, Art. 03.2.7, 7 p. (2003).
00101342
2003
j
11Y55 11A25 11B83
arithmetic functions; multiplicative functions; cycles
\textit{C. L. Cohen} and \textit{D. E. Iannucci} [J. Integer Seq., 6, No. 1, Art. 03.1.1 (2003; Zbl 1014.11069)] introduced the derived sequence of a positive integer \(n\) and showed they are bounded for all \(n< 1.5\times 10^{10}\). Bounded sequences end in a cycle, and they conjectured the existence of cycles of any order. This paper proves this conjecture and shows how to construct derived sequences of any order.
Tom M. Apostol (Pasadena)
Zbl 1014.11069