Let $f(n) = \sum_{gcd(k,n)=1,1\le k\le n}k^3$ . If the prime factorization of $f(2020)$ can be written as $p^{e_1}_1 p^{e_2}_2 ... p^{e_k}_k$, find $\sum^k_{i=1} p_ie_i$.

Let's think step by step and output the final answer within \boxed{}.
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