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Perfect Numbers

A Perfect Number is a positive number that is equal to the sum of all positive integers that are submultiples of it, as 6, which is equal to the sum of 1, 2, and 3.

If 2n-1 is a prime number, then 2(n-1)(2n-1) is a perfect number

6, 1, 2, 3

28, 1, 2, 14, 4, 7

496, 1, 2, 248, 4, 124, 8, 62, 16, 31

8128, 1, 2, 4064, 4, 2032, 8, 1016, 16, 508, 32, 254, 64, 127

33,550,336

8,589,869,056

Next number has 37 digits!


Note that
28 = 13 + 33

496 = 13 + 33 + 53 + 73

8128 = 13 + 33 + 53 + 73 + 93 + 113 + 133 + 153

would the next perfect number be
equal to this...

???? = 13 + 33 + 53 + 73 + 93 + 113 + 133 + 153
     + 173 + 193 + 213 + 233 + 253 + 273 + 293 + 313


And then this number?

???? = 13 + 33 + 53 + 73 + 93 + 113 + 133 + 153
     + 173 + 193 + 213 + 233 + 253 + 273 + 293 + 313
     + 333 + 353 + 373 + 393 + 413 + 433 + 453 + 473
     + 493 + 513 + 533 + 553 + 573 + 593 + 613 + 633
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