Analysis:

There are 1 and itself in the divisor of any natural number, and we call the factor smaller than itself the true divisor of this natural number. For example, all true divisors of 6 are 1, 2 and 3, and 6 = 1+2+3. In this way, the sum of all true divisors of a number is exactly equal to this number, which is usually called a perfect number.

The ancient Greeks attached great importance to perfect numbers. After Pythagoras discovered it, people began to study the perfect number. Maybe there are too few perfect numbers. So far, mathematicians have found 29 perfect numbers, all of which are even numbers. The first five perfect numbers are: 6,28,496,865,438+028, * * * * * * * *.

Perfect numbers have many interesting properties, such as the sum of continuous natural numbers:

6= 1+2+3

28= 1+2+3+4+5+6+7

8 128= 1+2+3+4……+ 127

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There is a wonderful relationship between natural numbers 220 and 284. The sum of all positive integers (excluding 220) of 220=22×5× 1 1 can be divided by1+2+4+5+10+20+65438. And the sum of all positive integers divisible by 284 (excluding 284) = 22× 7 1,1+2+4+71+142 is exactly equal to 220. This is a wonderful game! Mathematically, numbers with such characteristics are called "affinity numbers". Pythagoras discovered that 220 and 284 are the first pair of affinity numbers known to mankind, and they are also the smallest pair of affinity numbers.

1 184 and 12 10 are a pair of affinity numbers 2626 and 2924, 5020 and 5564.

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