# Cycles in Sums of Prime Factors

Cycles in Sums of Prime Factors

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.

sopfr

n

x↦sopfr(ax+b)

a

b