Question 29
Let $d(k)$ denote the number of positive divisors of a positive integer $k$. Prove that there exist infinitely many positive integers $M$ that cannot be written as
$$
M = \left( \frac{2 \sqrt{n}}{d(n)} \right)^2
$$
for any positive integer $n$.
$$
M = \left( \frac{2 \sqrt{n}}{d(n)} \right)^2
$$
for any positive integer $n$.