A PERFECT NUMBER IS WHOSE SUM OF DIVISORS IS EQUAL TO ITSELF, AND 6 IS A PERFECT NUMBER[dairy report] – Inishie R plusA –

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The divisors of 6 are 1, 2, and 3, and when you add these divisors together, you get 1+2+3=6, which is 6 itself. A perfect number is a number whose sum of divisors is equal to itself. 28 is a perfect number, and 6 too.

(Euclidean perfect number formula)

(2^p-1) is a prime number,2^p-1(2^p-1) is a perfect number.

When p=2, 2^2-1(2²-1)=2 x 3=6 (perfect number)

When p=3, 2^3-1(2³-1)=4 x 7 =28 (perfect number)

When p=4, 2^4-1(2⁴-1)=8 x 15 = 120 (not perfect, 15 is not prime)

When p=5, 2^5-1(2⁵-1)=16 x 31=496 (perfect number)

Can all perfect number formulas be expressed using Euclid’s perfect number formula? That is, all perfect numbers are2^p-1(2^p-1),and Is 2^p-1 a prime number?2000 years after Euclid’s death, Leonhard Euler showed that Euclid’s formula gives all the perfect even numbers.

(Euler’s perfect number theorem)If n is an even perfect number, then n is n=2^p-1(2^p-1), and  2^p-1 is a Mersenne prime.