If my calculations with my computer were rights, when I've consider the sequence of integers $n\geq 1$ satisfying $$\sigma(n)\mid (n(\sigma_0(n))^2),$$ where $\sigma(n)=\sum_{d\mid n}d$ is the sum of divisors function and $\sigma_0(n)=\sum_{d\mid n}1$ the number of such divisors, then such sequence starts as
1, 3, 6, 15, 28, 33, 42, 84, 91...
but I believe that such sequence isn't in The On-Line Encyclopedia of Integer Sequence.
Question. Are right my first terms? Is known such sequence in previous encyclopedia or are there references in the literature?
I've curiosity to know what's about the number of terms in the sequence for the first $10^k$ with $k=4,5,6,\cdots, N$, thats is a plot of the counting function for previous sequence.
Question. Can you provide us a graph of the counting function of such sequence for $10^N$, for a $N$ large? Thanks in advance.