Let $K$ and $L$ be two natural numbers. $K$ has $L$ divisors and $L$ has $\frac{K}{2}$ divisors.
How many divisors has $K+2L$ ?
2026-04-06 08:04:47.1775462687
Two natural numbers $K$ and $L$. $K$ has $L$ divisors, $L$ has $K/2$ divisors. How many divisors has $K+2L$?
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From the hint of Wojowu: There are at most $2\sqrt{n}$ divisors of $n$.
Thus, $L \le 2\sqrt{K}$ and $\frac{K}{2} \le 2\sqrt{L}$ implying $L^2 \le 16\sqrt{L}$. This follows $1 \le L \le 6$. From here you can find $K$ and then number of divisors of $K+2L$.