Equivalently, a perfect number is a number that is half the sum of all of its positive divisors (including itself) i.e. σ1(n) = 2n. So one can easily define an algorithm to check for perfect numbers :

Dec 5, 2019 · An odd perfect number n is of the form n = qkm2 n = q k m 2 where q q is prime and both q, k ≡ 1 mod 4 q, k ≡ 1 mod 4. Also, n satisfies σ(n) = 2n σ (n) = 2 n so that σ(qkm2) = 2qkm2 σ (q k …

Sep 4, 2017 · Odd perfect numbers do not exist. According to Euclid's formulae a perfect number is equal to $2^P(2^P-1$) where $2^P-1$ should be prime. Only $2$ is the even prime number and rest …

May 19, 2019 · 0 A square number can also be called a perfect square. So yes, the number 36 36 is a perfect square, because it is the product of 6 6 and itself.

Jun 6, 2014 · Explore related questions elementary-number-theory discrete-mathematics perfect-numbers See similar questions with these tags.

Jan 3, 2020 · A perfect number (integer) is equal to the sum of its divisors, including 1, and excluding itself. This has been around since Euclid. Recently, I noticed that at least for the initial integers, it is

Apr 23, 2020 · Euler proved that every even perfect number is of the form p(p+ 1)/2 p (p + 1) / 2 for p p a Mersenne prime, in particular it is equal to the p p -th triangular number (the sum 1+…+p 1 + + p) for …

Sep 3, 2017 · The following is a simplification of the proof that an odd perfect number cannot be divisible by 105 105 found here, as previously linked under the older Question to that effect. N =3m5n7k N = …

Questions about or involving perfect numbers which are positive integers that are equal to the sum of their proper positive divisors.

Mar 4, 2019 · Prove that every even perfect number is a triangular number. Ask Question Asked 6 years, 10 months ago Modified 6 years, 10 months ago