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Question 15

For a positive integer $$r$$, let $$[r]$$ denote the sum of its divisors other than $$1$$ and $$r$$ itself. For example, $$[6]=2+3=5$$. The value of $$[[[12]]]$$ is

Solution

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The proper divisors of $$12$$ other than $$1$$ are $$2,3,4,6$$, so $$[12]=15$$. Next, $$[15]=3+5=8$$. Finally, $$[8]=2+4=6$$, so $$[[[12]]]=6$$.

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