Let
denote the number of positive divisors of the positive integer
. Prove that there exist infinitely many positive integers
such that the equation
does not have a positive integer solution
.
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Let $\tau(n)$ denote the number of positive divisors of the positive integer $n$. Prove that there exist infinitely many positive integers $a$ such that the equation $\tau(an)=n$ does not have a positive integer solution $n$.