As $n$ ranges over the positive integers, what is the sum of all possible values of the greatest common divisor of $3n+4$ and $n$?
Applying Euclidean's algorithm, we get:
gcd(3n+4,n)=gcd(3n+4−3n,n)=gcd(4,n)
The factors of 4 are 1, 2, and 4. Sum them up and you'll get the answer.
