Marinada '22

[lang=hr] Miroslav nikako ne može shvatiti opsesiju svog prijatelja, ali kad god naiđe na neki zadatak od kojeg mu se izokrene želudac sjeti se Slavomirove kolekcije pa zadatak ljubazno proslijedi našem kolekcionaru. Evo jednog zadatka na koji je Miroslav nedavno naišao: \\Neka je $f(n)=\sum_{k = 1}^{100} \lfloor \log_{10} (kn) \rfloor$ za sve prirodni $n$. Koji je najveći $n$ takav da je $f(n)\leq 300$? [/lang] [lang=en] Miroslav doesn't get his firend's opsession, but anytime he stumbles upon a problem that makes him sick he remembers Slavomir's collection so he kindly sends the problem to our collector. Here is one problem that Miroslav recently found: \\Let $f(n)=\sum_{k = 1}^{100} \lfloor \log_{10} (kn) \rfloor$ for all positive integers $n$. Determine the greatest $n$ such that $f(n)\leq 300$? [/lang]