What doesn 2nd column depict in this table for perfect number description?

Question

I am reading about perfect number at below link.

http://mathworld.wolfram.com/PerfectNumber.html

I am not able to understand what does the 2nd column (p_n) depict?

n   p_n P_n  
1   2   6  
2   3   28  
3   5   496  
...  
....

Any help appreciated.

Answer 1

$p_n$ is the index. For $n=1$ we have $6=2^1(1+2)$, so $p_1=2$. For $n=2$ we have $28 = 2^2(1 + 2 + 2^2)$, so $p_2=3$. For $n=3$ we have $496 = 2^4(1 + 2 + 2^2 + 2^3 + 2^4)$, so $p_3=5$. Do you see the pattern ? If not, here one more example: $8128 = 2^6(1 + 2 + · · · + 2^6)$, so $p_4=7$.