Given two numbers m and n, if the sum of all factors except m itself is equal to n, and the sum of all factors except n itself is equal to m, we call m and n a pair of affinity numbers. Pythagoras in the 6th century BC first discovered the first pair of affinity numbers 220 and 284, because 220 = 1+2+4+7 1+64. 284 =1+2+4+5+10+1+20+22+44+55+10. Affinity number is named because it symbolizes friendship.

I found the interval between the second pair of affinity numbers and the first pair of affinity numbers is so long! It was not until 1636 that Fermat discovered the second pair of affinity numbers, 17296 and 184 16. The Arabic mathematician Tabit Ibn gave a rule for finding affinity number: n > 1, if a = 3.2n- 1. Since c = 9.22n- 1- 1 are both prime numbers, 2nab and 2nc are a pair of affinity numbers. For example, when n=2, 220 and 284 are generated. The third pair of affinity numbers was put forward by Descartes in 1638: 936384 and 9389. 1999999995. Later, people verified that there were two pairs of right and wrong. In 1866, Nicholas found that 1 184 and 12 10 are a pair of affinity numbers, which is very interesting. People have been looking for affinity numbers since the Greek period, and countless mathematicians have spent a lot of energy and painstaking efforts to find much larger affinity numbers.

Now people have known thousands of pairs of affinity numbers, the largest of which is two numbers 152 found by Lyle in 1974: m = 34. 5.11.528119.