Perfect Number?

Question

A perfect number is a counting number that is equal to the sum of all its counting number divisors except itself. For example, 28 is a perfect number, since its divisors other than itself are 1,2,4,7,14: 1+2+4+7+14 = 28. What is the next perfect number greater than 28.

Answer 1

496.
factors are :1, 2, 4, 8, 16, 31, 62, 124, 248

8128 is the next perfect number after it. I used a script just like the guys above me. Run it in Matlab and you'll get it.
---
for N = 29:500
Sn = 0;
test = 0;

for n = 1:N-1
if mod(N,n) == 0
Sn = Sn + n;
end
end
if Sn == N
test = 1;
value = N;
N = 500;
end
end
disp(value);
---

Answer 2

It is an open question whether any odd perfect numbers exist.

Euclid proved about 2500 years ago that every even perfect number corresponded to what we now call a "Mersenne prime", being a prime number of the form (2^p - 1).

The first few Mersenne primes are 3, 7, 31, 127, . . .

The corresponding perfect numbers are 3 * 2 = 6, 7 * 4 = 28, 31 * 16 = 496, 127 * 64 = 8128, . . .

It is easier to see the correspondence than to write down the algebraic expression for it.

Answer 3

496

Answer 4

496