A reminder of the prime factorization of the New Year

So, fun fact of the year. The prime factorization of $2014$ is $2 \cdot 19 \cdot 53$ . Thus, the sum of the positive divisors of $2014$ is

$(1+2) \cdot (1+19) \cdot (1+53) = 3 \cdot 20 \cdot 54 = 2^3 \cdot 3^4 \cdot 5,$

so the answer is $4 \cdot 5 \cdot 2 = \boxed {40}$ .