this post was submitted on 06 Jun 2024
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31521281 = 11 × 17 × 59 × 2857
11 × 17 = 187
11 × 59 = 649
11 × 2857 = 31427
17 × 59 = 10003
17 × 2857 = 48569
59 × 2857 = 168563
17 × 59 × 2857 = 2865571
11 × 59 × 2857 = 1854193
11 × 17 × 2857 = 534259
11 × 17 × 59 = 11033
11+17+59+2857+11033+534259+1854193+2865571+168563+ 48569+10003+31427+649+187=5527398≠31521281
you've got an extra zero in there, and you forgot the 1, but the rest of your divisors match my crude brute-force approach:
same conclusion though: 5518399 also ≠ 31521281
bonus nonsense
(from https://oeis.org/A000396 i see the next perfect number after 8128 is 33550336 which is too big for me to wait for the naive approach above to test...) spoiler more bonus nonsense
:::
What about 2^31521281 - 1, I'm pretty sure that's a perfect odd number