# Product is Sum, Sum is Product

Number Theory Level 1

$\displaystyle \sum_{i=1}^n a_{n} = \displaystyle \prod_{i=1}^{n} a_{n}$

What is the maximum value of $$n$$ such that there exists a sequence of natural numbers $$a_{1}, a_{2}, \ldots a_{n}$$ satisfying the equation above?

×