Amicable numbers

Two different natural numbers $a < b$ are called amicable if the sum of the divisors of $a$ (other than $a$) equals $b$ and the sum of the divisors of $b$ equals $a$. For example, $220$ and $284$: $1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284$, $1 + 2 + 4 + 71 + 142 = 220$.

You are given a natural number $n$. Find all amicable pairs with both numbers not exceeding $n$.

A single integer $n$ ($1 \le n \le 2 \cdot 10^4$).

Each pair on its own line: $a$ and $b$ ($a < b$), in increasing order of $a$. If there are no pairs — 0.

It is convenient to move the inner loop that sums the divisors into a function: find $b = s(a)$ and check that $a < b \le n$ and $s(b) = a$. It is enough to check divisors up to $\sqrt{x}$, not up to $x$: if $d$ is a divisor, so is $x / d$. Write the condition as d * d <= x.