# zbMATH — the first resource for mathematics

Further results on derived sequences. (English) Zbl 1058.11080
C. L. Cohen and 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.
##### MSC:
 11Y55 Calculation of integer sequences 11A25 Arithmetic functions; related numbers; inversion formulas 11B83 Special sequences and polynomials
##### Keywords:
arithmetic functions; multiplicative functions; cycles
Full Text: