# On integers having a given number of divisors

I have a nice question for you today =).

For a natural number $n\geq 2$, define $f(n)$ to be the smallest positive integer which has exactly $n$ positive divisors. Show that for any $k\geq 0$, the number $f(2^{k})$ divides the number $f(2^{k+1})$

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