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: $\boxed{220, 284, 1184, 1210, 2620, 2924, 5020, 5564, 6232, 6368, 10744, 10856, 12285, 14595, 17296, 18416, 63020, 66928, 66992, 76084}$