Given natural numbers $M$ and $N$, I'd like to find a partition of $2^N$ with $M$ or fewer terms, $t_1 + t_2 + ... + t_M$, such that $\max(\phi(t_1), \phi(t_2), ..., \phi(t_M))$ is minimized, where $\phi$ is Euler's totient function.
What might a smart algorithm for this look like? I can approach this with raw CPU power and metaheuristic search, but maybe the partition can be found analytically? I am mostly interested in $N$ = 8, 16, 32, 64, 128 in case that somehow simplifies the problem.