Find the smallest positive integer that is exactly half the sum of its proper divisors?

Question

We are given a positive integer N. Two of its positive divisors are chosen and the differences between N and these two divisors are 270 and 280 respectively.

Find the number of possible value(s) of N?

Answer 1

The first/smallest perfect number is 6.
Its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. The number 6 is equal to half the sum of all its positive divisors: (1+2+3+6)/2=6.
Note-- The next perfect number is 28--> 28=1+2+4+7+14. This is followed by 496 and 8128