Perfect number

A perfect number is a number that is half the sum of all of its positive divisors, and it is including itself.

σ(N)=2N

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28 is the perfect number.

28=1 + 2 + 4 + 7 + 14

σ(28)=1 + 2 + 4 + 7 + 14 + 28 = 2*28 = 56

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Euler proved that all even perfect numbers were in the Euclid–Euler theorem.

The sum of divisors of a number must include the number itself, not just the proper divisors.

σ(2^2(2^3-1))=σ(4)σ(7)=(1+2+4)(1+7)=7*8=56=σ(28)

This is known as Mersenne primes.

2(2^2-1)=6

2^2(2^3-1)=28

2^4(2^5-1)=496

These are perfect numbers.

3,7,31 are primes, so you can find perfect numbers infinitely because of fractal. However, odd perfect numbers are unknown.