[seqfan] Re: A007357 infinitary perfect number b-file

Richard Mathar mathar at strw.leidenuniv.nl
Wed Mar 30 12:32:46 CEST 2011

and the information currently in http://oeis.org/A007357

vs> ...
vs> I published a list of all 36 such numbers up to 2^16 by name "Fermi-Dirac perfect numbers".
vs> ...
If "such numbers" refers to A007357 it means that these first 4 of these
numbers were calculated, which is basically irrelevant. If "such numbers"
refers to A050376, I do not see how there are only 36 in the range up to 2^16.

vs> and I learned that J. M. Pedersen in "Tables of Aliquot Cycles." http://amicable.adsl.dk/aliquot/infper.txt. " in 2004 calculated the first 155 iperfect numbers.

The Pedersen table in http://amicable.adsl.dk/aliquot/i1/i1.txt is annotated
with "Perfect numbers, exhaustive below 5*10^12"  in http://amicable.adsl.dk/aliquot/tables.htm
This gives rich opportunity to some sort of standard misinterpretation to 
some readers that this table were complete up to its last member listed. We
have had this sort of trouble with OEIS submissions concerning Mersenne
numbers and other cases, where the list of known candidates reaches far beyond
the highest watermark of the dense lists.
Here, the current entries in A007357 reach up to 3*10^16, further than
the Pedersen high watermark. The answer to my original question in
http://list.seqfan.eu/pipermail/seqfan/2011-March/014687.html is
"No, we should not copy more numbers from the Pedersen table to A007357."

Richard Mathar

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