The number 8 is the sum and product of the numbers in the collection of four positive integers \{1,1,2,4\}, since 1+1+2+4=8 and 1\times1\times2\times4=8. The number 2007 can be made up from a collection of n positive integers that multiply to 2007 and add to 2007. What is the smallest value of n with n>1?
Answer Choices
A. 1171
B. 1337
C. 1551
D. 1777
E. 1781