I do not understand how it works. If we said 33 was a prime, then σ(4488) = σ(8*17*33) = σ(8)*σ(17)*σ(33) =! 15*18*34 = 9180 (under the false hypothesis "!" that 33 is prime). I cannot see how that should give a perfect number, σ(x) = 2*x. The "prime factor" 33 which appears in 2*x, does not arise in σ(x).
Also note that Euler proved all even perfect numbers are of Euclid's classical form (i.e. perfect numbers arising from Mersenne primes). Therefore, no perfect number can have the form 2^n * a * b where n is greater than zero, and a and b are greater than one.
/JeppeSN
