What comes next?

[Thomas Klemm]

The sequence of perfect numbers grows fast: A000396.
Therefore, only the first 6 or 7 can be displayed.

Here's a program for the HP-42S that calculates \(2^{p-1} \cdot \left( 2^p -1 \right)\):

Code:

00 { 13-Byte Prgm }
01 2
02 ENTER
03 1/X
04 X<> ST Z
05 Y↑X
06 ×
07 LASTX
08 1
09 -
10 ×
11 END

Just use it with the first primes but skip 11 since \(2^{11}-1=2047=23\times89\) is not a prime.

Examples

2 R/S
6

3 R/S
28

5 R/S
496

7 R/S
8'128

13 R/S
33'550'336

17 R/S
8'589'869'056

19 R/S
137'438'691'328