Majestic Perfect Numbers

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Definition: Perfect numbers are numbers that whose sum of its divisors (excluding itself) equals the number itself.

A neat example would be 66 :

Courtesy of Wikipedia Courtesy of Wikipedia

The next perfect numbers are 28,496,812828, 496, 8128 \dots. There are 5050 known perfect numbers as of January 20182018. Euclid proved a formation rule whereby q(q+1)2\dfrac{q(q+1)}{2} is an even perfect number whenever qq is a Mersenne Prime (of the form: 2n12^n-1). The formula for an even perfect number is 2p1(2p1)2^p-1(2^{p-1}) where pp and 2p12^p-1 are prime. It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist.


There are other variations of perfect numbers like Triperfect numbers, Quasiperfect numbers and many more! Sadly, the list of these variations have an ending and no ore of these have been found.

Note by Mohmmad Farhan
1 year ago

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A little suggestion :

Please try to post any note completely and fully as much as possible. If it is a time taking process then write as much as you can and save that in Microsoft word. When the whole note is completed then paste the whole thing at once and post it.

Ram Mohith - 1 year ago

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