Perfect numbers, please help Perfect numbers:6, 28, 496, 8128, ...
There is some interesting patterns, I just want to share it with you guy and ask some questions about.
(1)
$1+2+3=6$, perfect number 6 has 3 terms
$\frac{3-1}{2}=1$
$$6=1\cdot2\cdot3$$
(2)
$1+2+4+7+14=28$, has 5 terms
$\frac{5-1}{2}=2$
$$28^2=1\cdot2\cdot4\cdot7\cdot14$$
(3)
$1+2+4+8+16+31+62+124+248=496$, has 9 terms
$\frac{9-1}{2}=4$
$$496^4=1\cdot2\cdot4\cdot8\cdot16\cdot31\cdot62\cdot124\cdot248$$
This is resembling the factorial numbers. 
I want to know does this pattern continue for all perfect numbers? If it does how you go about justifying it.

That's not a coincidence. The divisors of any (non-perfect-square) number $n$ are paired together: any time you have a divisor $d$, you have $n/d$ which is the other divisor, in some sense, his brother.
For example, for $n=496$
$$1 \cdot 2 \cdot 4 \cdot 8 \cdot 16 \cdot 31 \cdot 62 \cdot 124 \cdot 248 =$$
$$=(2 \cdot 248) \cdot (4 \cdot 124) \cdot (8 \cdot 62) \cdot (16 \cdot 31)= 496^4$$
How is that the power is $4$? That's because there are $9$ divisors, and you throw away the trivial divisor $1$ (whose brother is $496$). The remaining $8$ divisors are paired, and you get $4$ pairs of numbers whose product is $496$.
