yujhtheyujh Contest 1 - P1

Contributed by: yujhtheyujh

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Difficulty: 9

This problem is tagged with yty, yty1.

A function $f$ is defined such that $f(0) = 0$ and for all $i \gt 0$, $f(i) = i - (\text{smallest prime factor of i})$. Someone applied $f$ to a number $N$ exactly $K$ times such that the resulting number is exactly $2023$ less than $N$. Find the least $N$ when $K$ is minimized. Note that $f(1)=1$.

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