Product-sum number
= 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 $k\ge2$, the example $2,k$ with $k-2$ ones proves that the smallest product-sum value is at most $2k$.