OPENHARDnumber theorydivisorsfactorials
We call $m$ practical if every integer $1 \leq n < m$ is the sum of distinct divisors of $m$. If $m$ is practical let $h(m)$ be such that $h(m)$ many divisors always suffice. Is it true that $h(n!)<(\log n)^{O(1)}$?
Notes: Erdos showed h(n!) < n. Vose proved existence of infinitely many practical m with h(m) << (log m)^{1/2}.
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