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-   -   Might miss small sociable number (https://www.mersenneforum.org/showthread.php?t=26867)

sweety439 2021-06-02 07:00

Might miss small sociable number
 
OEIS sequence [URL="https://oeis.org/A003416"]https://oeis.org/A003416[/URL] may not be complete to 1799281330, also the site [URL="http://djm.cc/sociable.txt"]http://djm.cc/sociable.txt[/URL], since it is not even known whether 56440 is a member of sociable number, however, if so, the length of the cycle of 56440 must be >5000

Reference: [URL="http://factordb.com/sequences.php?se=1&aq=56440&action=last20&fr=0&to=100"]http://factordb.com/sequences.php?se=1&aq=56440&action=last20&fr=0&to=100[/URL]

Note that the Aliquot sequence of 1578 merges with that of 56440

LaurV 2021-06-02 07:18

I believe 276 is a "social distance" number.

That means it is a social number, but it will be a long distance till somebody will find out that the sequence 276 ends in 276. :razz:

(edit: or we can have a cycle that includes all [URL="https://en.wikipedia.org/wiki/Aliquot_sequence#Catalan%E2%80%93Dickson_conjecture"]Lehmer's Five[/URL], why not? hehe).

So, yeah, you are right, those OEIS sequences are not complete...

[COLOR=White](Oh Dear Mighty God, he is back...)[/COLOR]

sweety439 2021-06-02 07:40

[QUOTE=LaurV;579746]I believe 276 is a "social distance" number.

That means it is a social number, but it will be a long distance till somebody will find out that the sequence 276 ends in 276. :razz:

(edit: or we can have a cycle that includes all [URL="https://en.wikipedia.org/wiki/Aliquot_sequence#Catalan%E2%80%93Dickson_conjecture"]Lehmer's Five[/URL], why not? hehe).

So, yeah, you are right, those OEIS sequences are not complete...

[COLOR=White](Oh Dear Mighty God, he is back...)[/COLOR][/QUOTE]

276 is not possible in a sociable cycle, since it is an untouchable number ([URL="https://oeis.org/A005114"]https://oeis.org/A005114[/URL])

LaurV 2021-06-02 07:59

Doh, you got me there!
:picard:

Stargate38 2021-06-03 17:20

Maybe a later term will be the cycle's start. We don't know if that'll happen yet, but the later terms aren't untouchable. Other sequences (i.e. 10000018198 and 31657014970784) merge with 276.

sweety439 2021-06-08 16:14

See related thread [URL="https://mersenneforum.org/showthread.php?t=22701"]https://mersenneforum.org/showthread.php?t=22701[/URL]

[color=red][b]MODERATOR NOTE:[/b] Following five posts moved there[/color]

Happy5214 2021-09-21 11:16

Whatever the prior research, the second half of this thread looks more like a blog thread than anything that should stay in the Aliquot forum. Perhaps these posts should be moved over to the "sweety's Musings" section.


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