Two numbers are said to be amicable if each number is the sum of the proper divisors of the other.

A proper divisor of a number is any divisor of the number except the number itself.

For example, the proper divisor of 12 are 1, 2, 3, 4, and 6.

Notice that 12 is not included in the list although it is a divisor of 12.

Now we will show that 220 and 284 are amicable numbers.

The proper divisors of 284 are 1, 2, 4, 71, and 142

1 + 2 + 4 + 71 + 142 = 220

The sum of the proper divisors of 284 is equal to 220

The proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110

1 + 2 + 4 + 5 + 10 + 11 + 20 + 22 + 44 + 55 + 110 = 284

The sum of the proper divisors of 220 is equal to 284.

Therefore, we can conclude that 220 and 284 are amicable numbers.

A short list of amicable numbers are shown below

220 284

1184 1210

2620 2924

5020 5564

6232 6368

10744 10856

12285 14595

......

.......

437456 455344

469028 486178

503056 514736

522405 525915

600392 669688

609928 686072

Let us show that 600392 and 669688 are amicable

Use this calculator to quickly see the factors. That way you don't have to waste time.

The proper factors of 609928 are 1, 2, 4, 8, 11, 22, 29, 44, 58, 88, 116, 232, 239, 319, 478, 638, 956, 1276, 1912, 2552, 2629, 5258, 6931, 10516, 13862, 21032, 27724, 55448, 76241, 152482, and 304964

Add all the numbers and it will equal to 686072

The proper factors of 686072 are 1, 2, 4, 8, 191, 382, 449, 764, 898, 1528, 1796, 3592, 85759, 171518, and 343036

Add all the numbers above and you will get 600392

600392 and 669688 are indeed amicable