MathNet 2021 — Part 09 Question 78

Let $N$ be the positive integer $7777\ldots777$, a $313$-digit number where each digit is a $7$. Let $f(r)$ be the leading digit of the $r$th root of $N$. What is $f(2) + f(3) + f(4) + f(5) + f(6)$?