HMMT 2007 U9

I ponder some numbers in bed,

All products of three primes I've said, Apply $\phi$ they're still fun: now Elev'n cubed plus one.

$$\begin{gathered} n=37^{2} \cdot 3 \ldots \\ \phi(n)= \\ 11^{3}+1 ? \end{gathered}$$

What numbers could be in my head?