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Cycles in Sums of Prime Factors

​
n
66
a
8
b
1
view
numbers
plot
allow numbers to grow
Define the function
sopfr
that is the sum of the prime factors of
n
. The iteration of
x↦sopfr(ax+b)
invariably (for the numbers explored) leads to closed loops of varying length for integers
a
and
b
. 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.
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