Product-sum number

A positive integer $N$ that is both the sum and the product of one multiset of $k$ positive integers. For factors at least $2$ with product $P$, sum $S$, and count $t$, appending $P-S$ ones gives $k=t+P-S$ without changing the product. For $k\ge 2$, the example $2,k$ with $k-2$ ones proves that the smallest product-sum value is at most $2k$.