2004 AIME I Problems/Problem 15
Problem
For all positive integers let
![$f(x)=\begin{cases}1 & \rm{if \ x=1}\\ \frac x{10} & \rm{ if \ x \ is \ divisible \ by \ 10}\\ x+1 & \rm{otherwise}\end{cases}$](http://latex.artofproblemsolving.com/7/c/7/7c7b21e10a1b0c4d13e74105fd79da4bc36b79f0.png)
and define a sequence as follows: and
for all positive integers
Let
be the smallest
such that
(For example,
and
) Let
be the number of positive integers
such that
Find the sum of the distinct prime factors of