# Ramanujan would like it

Number Theory Level 4

$\large\color{Violet}3^{ \color{green}n}+ \color{Violet}3^{\color{green}n-\color{Brown}1}+ \color{Violet}3^{\color{green}n-\color{Brown}2}+ \color{Violet}3^{\color{green}n-\color{Brown}3}+\color{Violet}3^{\color{green}n-\color{Brown}4}$

For a certain $$n$$ the expression above has $$5178$$ positive divisors (inclusive of $$1$$ and itself), compute $$n$$.

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