Identify the first 20 friendly or amicable numbers.

Two distinct positive integers $a$ and $b$ are called amicable numbers (or friendly numbers) if the sum of the proper divisors of $a$ is equal to $b$, and the sum of the proper divisors of $b$ is equal to $a$. The proper divisors of a number include all its positive divisors except the number itself.

Let $\sigma(n)$ denote the sum of all positive divisors of $n$. Then the sum of the proper divisors of $n$ is $\sigma(n) - n$.
So, $a$ and $b$ are amicable if $\sigma(a) - a = b$ and $\sigma(b) - b = a$.

For example, consider the first amicable pair $(220, 284)$:

• The proper divisors of 220 are $1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110$. Their sum is $1+2+4+5+10+11+20+22+44+55+110 = 284$.
• The proper divisors of 284 are $1, 2, 4, 71, 142$. Their sum is $1+2+4+71+142 = 220$. Since the sum of the proper divisors of 220 is 284, and the sum of the proper divisors of 284 is 220, the numbers 220 and 284 form an amicable pair.

The first 20 amicable numbers (derived from the first 10 amicable pairs, listed in ascending order) are:

• 220
• 284
• 1184
• 1210
• 2620
• 2924
• 5020
• 5564
• 6232
• 6368
• 10744
• 10856
• 12285
• 14595
• 17296
• 18416
• 63020
• 66928
• 66992
• 76084

The first 20 friendly or amicable numbers are:
$\boxed{\text{220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 76084}}$