Friendly numbers

If two numbers have the same abundancy, then they are called Friendly Numbers.

There are three steps in calculating friendly numbers:

1. Find the list of all factors (even non prime) of a number.
2. Find the sum of all those factors.
3. Divide the sum of all the factors by that number itself.

For example, for 30,

1. List of all factors is: 1, 2, 3, 5, 6, 10, 15, 30
2. Sum of all factors is: 1 + 2 + 3 + 5 + 6 + 10 + 15 + 30 = 72
3. Divide 72 by 30, so we get 12/5.

12/5 is called the abundancy of the number 30.

Again, we repeat:

If two numbers have the same abundancy, then they are called Friendly Numbers.

140 has the same abundancy (= 12/5) as 30, and therefore 140 and 30 are called friendly numbers.

Calculating the abundancy of 140:

1. List of all factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140
2. Sum of all factors: 1 + 2 + 4 + 5 + 7 + 10 + 14 + 20 + 28 + 35 + 70 + 140 = 336
3. Divide 336 by 140, so we get 12/5.

Therefore both 30 and 140 have got the same abundancy (= 12/5) and this is why they form a pair of Friendly Numbers.

Similarly, all other numbers which have the same abundancy are called friendly numbers.\

List of Friendly Numbers (first 20)

(6, 28), (30, 140), (80, 200), (40, 224), (12, 234), (84, 270), (66, 308), (78, 364), (102, 476), (6, 496), (28, 496), (114, 532), (240, 600), (138, 644), (120, 672), (150, 700), (174, 812), (135, 819), (186, 868), (864, 936), (222, 1036), (246, 1148)