Let f(n) = \sum\limits_{\gcd(k,n)=1,1 \leq k \leq n} k^3. If the prime factorization of f(2020) can be written as p_1^{e_1}p_2^{e_2} \cdots p_k^{e_k}, find \sum\limits_{i=1}^{k} p_i e_i.
Let f(n) = \sum\limits_{\gcd(k,n)=1,1 \leq k \leq n} k^3. If the prime factorization of f(2020) can be written as p_1^{e_1}p_2^{e_2} \cdots p_k^{e_k}, find \sum\limits_{i=1}^{k} p_i e_i.