An iteration problem involving the divisor function
Claudia Spiro (1986)
Acta Arithmetica
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Claudia Spiro (1986)
Acta Arithmetica
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Sinyor, Joseph (2010)
International Journal of Mathematics and Mathematical Sciences
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Marcus Nilsson (2000)
Annales mathématiques Blaise Pascal
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Jeffrey Lagarias (1990)
Acta Arithmetica
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Michal Křížek, Lawrence Somer (2004)
Mathematica Slovaca
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Li, Xiaoqin (2009)
Journal of Integer Sequences [electronic only]
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Lewittes, Joseph (2007)
Integers
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Bryant, Darryn, Gavlas, Heather, Ling, Alan C.H. (2003)
The Electronic Journal of Combinatorics [electronic only]
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Lawrence Somer, Michal Křížek (2004)
Czechoslovak Mathematical Journal
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We assign to each positive integer a digraph whose set of vertices is and for which there is a directed edge from to if . We establish necessary and sufficient conditions for the existence of isolated fixed points. We also examine when the digraph is semiregular. Moreover, we present simple conditions for the number of components and length of cycles. Two new necessary and sufficient conditions for the compositeness of Fermat numbers are also introduced.