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Algebra Level 4

For all positive integers x, let f(x) = 1 if x = 1, f(x) =x/10 if x is divisible by 10, f(x) = x + 1 otherwise, and define a sequence of integers as follows: x1 = a and x{n+1} = f(xn) for all positive integers n. Let d(a) be the smallest n such that xn = 1. (For example, d(100) = 3 and d(87) = 7.) Let m be the number of positive integers b such that d(b) = 20. Find the sum of the distinct prime factors of m. Source: AOPS

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