SCHWEITZER 2018 Problem 5

For every positive integer $n$ , define $$f(n)=\sum_{p\mid n}{p^{k_p}},$$ where the sum is taken over all positive prime divisors $p$ of $n$ , and $k_p$ is the unique integer satisfying $$p^{k_p}\leqslant n<p^{k_p+1}.$$ Find $$\limsup_{n\to \infty} \frac{f(n)\log \log n}{n\log n} .$$