Calculating product of totient functions
Let $p=500009$ and $m=12p+1$. One possibility is to use the fact that $\phi(m) \equiv 0 \pmod{p}$, and hence it's enough to pre-calculate all values up to $m$. Storing each answer in a 32-bit integer, this is a table of size 24MB.

If you don't like pre-calculating everything, you can use in some other way the fact that only numbers below $m$ need to be considered. Be creative.