And the rest of the 'proof' is thus:
Let the number be n
We know that two of the 4 smallest divisors will be 1 and 2.
If another is 3, then we have n = 1 + 4 + 9 + a^2 = 14 + a^2. a/n, so a/14 (as a/a^2). We check 7 and 14, and they don't work.
Therefore 3 does not divide n
We check...