What is the sum of the prime factors of $2^{16}-1$? I know $2^{10}=1024$ and $2^6=64$, but it seems they are not very helpful in solving this problem. There must be a trick to solve the problem in an easy way. 

What is the sum of the prime factors of $2^{16}-1$?


Using $a^2-1=(a-1)(a+1)$ we have:
$$2^{16}-1=(2^8-1)(2^8+1)=(2^4-1)(2^4+1)(2^8+1)=15\cdot 17\cdot 257=3\cdot 5\cdot 17\cdot 257$$
So, the answer is $3+5+17+257=282$.
