Cycles in Sums of Prime Factors

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Define the function that is the sum of the prime factors of . The iteration of invariably (for the numbers explored) leads to closed loops of varying length for integers and . On the graph, the red dot indicates the beginning of the current cycle. It is not known if every iteration is eventually periodic, or if there is a finite number of limit cycles.

Contributed by: Enrique Zeleny (March 2011)
Open content licensed under CC BY-NC-SA




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