For any integer
let
be the smallest possible integer that has exactly
positive divisors (so for example we have
and
). Prove that for every integer
the number
divides
Proposed by Suhaimi Ramly, Malaysia
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For any integer $d > 0,$ let $f(d)$ be the smallest possible integer that has exactly $d$ positive divisors (so for example we have $f(1)=1, f(5)=16,$ and $f(6)=12$). Prove that for every integer $k \geq 0$ the number $f\left(2^k\right)$ divides $f\left(2^{k+1}\right).$
Proposed by Suhaimi Ramly, Malaysia
Školjka