3. Decompose 2017 into the sum of several unequal positive integers, then the maximum value of the product of the decomposed numbers is
3. $4 \cdot 3^{671}$

Analysis: Consider $4=2+2=1+3$, and $2 \times 2>3, 5=2+3=1+4$, and $2 \times 3>4$. For positive integers not less than 6, since $2+2+2=3+3$, and $2^{3}<3^{2}$, it is optimal to decompose a number into a sum of several 3s to maximize the product of the decomposition. Also, $2017=3 \times 672+1=3 \times 671+4$. From the above analysis, the maximum value is $4 \cdot 3^{671}$.