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Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself. In symbols, 1(n) = 2n where 1 is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 + 28 = 56 = 2 × 28. What is now called a Presence prime.
A number is perfect if the sum of its proper factors is equal to the number. To find the proper factors of a number, write down all numbers that divide the number except the number itself. If the sum of the factors is equal to 18, then 18 is a perfect number.
There are only 2 perfect numbers from 1 to 100 which are 6 and 28.
Here double proportion means that each number is twice the preceding number, as in 1, 2, 4, 8, For example, 1 + 2 + 4 = 7 is prime. Therefore, 7 × 4 = 28 (the sum multiplied into the last) is a perfect number.
But we subtract 1 from each of those numbers because we are multiplying (2p-1) by (2p 1). That translates into either multiplying a number ending in 6 by (1=2-1), which will end in 6 or a number ending in 4 by (7= 8-1), whose result will end in 8.
The first 5 perfect numbers are 6, 28, 496, 8128, and 33550336.
A perfect number is defined to be one which is equal to the sum of its liquor parts. The four perfect numbers 6, 28, 496 and 8128 seem to have been known from ancient times and there is no record of these discoveries.
Perfect number. Perfect number, a positive integer that is equal to the sum of its proper divisors. The smallest perfect number is 6, which is the sum of 1, 2, and 3. Other perfect numbers are 28, 496, and 8,128.
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