This is the sequence of what are called "perfect" integers.

A perfect integer is one which equals to the sum of all its factors
except itself.

The factors of 6, not including 6 are 1,2,3 and sure enough,
1+2+3=6.

The factors of 28, not including 28 are 1,2,4,7,14 and sure enough,
1+2+4+7+14 = 28

The factors of 496, not including 496 are 1,2,4,8,16,31,62,124,248 and
sure enough, 1+2+4+8+16+31+62+124+248 = 496

The factors of 8128, not including 8128 are 1,2,4,8,16,32,64,127,254,508,1016,2032,4064 and
sure enough, 1+2+4+8+16+32+64+127+254+508+1016+2032+4064 = 8128

The next perfect integer is 33550336
The factors of 33550336, not including 33550336 are
1,2,4,8,16,32,64,128,256,512,1024,2048,4096,8191,16382,32764,65528,
131056,262112,524224,1048448,2096896,4193792,8387584,16775168
and sure enough,
1+2+4+8+16+32+64+128+256+512+1024+2048+4096+8191+16382+32764+65528+
131056+262112+524224+1048448+2096896+4193792+8387584+16775168 = 33550336

Edwin