Take the tour ×  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.  share|improve this question Here's a
suggestion, I don't know how good it is. Precompute a list of
"sparsely totient numbers," see oeis.org/A036913. Given $N$,
find the largest sparsely totient number $x$ not exceeding
$2^N$, let $t_M=x$, then apply recursively to $2^N-x$ to get
$t_{M-1},\dots,t_2$, then let $t_1$ be whatever's left over.
Maybe instead of largest s.t.n not exceeding $2^N$, use largest
s.t.n not exceeding $2^N/M$. –  Gerry Myerson Jan 18 at 4:46 It
maybe a great idea. I read that the ith p