Question 60
Let $d(n)$ denote the number of positive divisors of $n$. For positive integer $n$ we define $f(n)$ as
$$
f(n) = d(k_1) + d(k_2) + d(k_3) + \dots + d(k_m),
$$
where $1 = k_1 \lt k_2 \lt \dots \lt k_m = n$ are all divisors of the number $n$. We call an integer $n \gt 1$ almost perfect if $f(n) = n$. Find all almost perfect numbers.
$$
f(n) = d(k_1) + d(k_2) + d(k_3) + \dots + d(k_m),
$$
where $1 = k_1 \lt k_2 \lt \dots \lt k_m = n$ are all divisors of the number $n$. We call an integer $n \gt 1$ almost perfect if $f(n) = n$. Find all almost perfect numbers.