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# Problem 641

## A Long Row of Dice

Consider a row of $n$ dice all showing $1$.

First turn every second die,$(2,4,6,\ldots)$, so that the number showing is increased by $1$. Then turn every third die. The sixth die will now show a $3$. Then turn every fourth die and so on until every $n$th die (only the last die) is turned. If the die to be turned is showing a $6$ then it is changed to show a $1$.

Let $f(n)$ be the number of dice that are showing a $1$ when the process finishes. You are given $f(100)=2$ and $f(10^8)=69$.

Find $f(10^{36})$.