Interesting facts about the number 28

I really like numbers with special properties and today I would like to share with you why the number 28 is really a special number.

Perfect number

A number is perfect if it contains all positive factors except itself.
28 = 1+2+4+7+14
This alone is a really cool property. The three smallest perfect numbers are 6, 28, 496. As you can quickly see perfect numbers are seldom.

Sociable numbers

A number is a social number if the aliquot sum (the sum of all proper divisors except the number itself) if it forms a cyclic sequenc that begins and ends with the same number.
This might sound complex at first but let us start with a simple example.
Will do the example with a period of 4.

Sum of all proper divisors of 1264460

1 + 2 + 4 + 5 + 10 + 17 + 20 + 34 + 68 + 85 + 170 + 340 + 3719 + 7438 + 14876 + 18595 + 37190 + 63223 + 74380 + 126446 + 252892 + 316115 + 632230 = 1547860

Sum of all proper divisors of 1547860

1 + 2 + 4 + 5 + 10 + 20 + 193 + 386 + 401 + 772 + 802 + 965 + 1604 + 1930 + 2005 + 3860 + 4010 + 8020 + 77393 + 154786 + 309572 + 386965 + 773930 = 1727636

Sum of all proper divisors of 1727636

1 + 2 + 4 + 521 + 829 + 1042 + 1658 + 2084 + 3316 + 431909 + 863818 = 1305184

Sum of all proper divisors of 1305184

1 + 2 + 4 + 8 + 16 + 32 + 40787 + 81574 + 163148 + 326296 + 652592 = 1264460.

As you can see the number we started with is the same we got in the end. The number 1264460 is a social number with period 4.

But where's the link to the number 28?

Currently the largest known social number is a number with period 28! So instead of doing what I've done above 4 times you have to do it 28 times to get the same number again. In fact perfect numbers and social numbers are closely related!
This is just beautiful.