[seqfan] Re: Numbers with sigma(n)/n a rational power

William Keith william.keith at gmail.com
Sat Nov 2 16:27:10 CET 2013


     The comment that you put in to that sequence is a nice method of
finding new entries, although it doesn't guarantee that there are not
smaller entries with the same property.  You should add the additional
numbers you have found to the sequences of appropriate powers, with the
notation that the sequences may be incomplete -- i.e., we can obtain large
entries but smaller entries may still be found.  It would also be
appropriate if you, or someone knowledgeable about abundancies, could add a
comment that as of some date the list was known to be complete up to a
given bound.

     As for your latter question, I would suggest making a new sequence by
simply going through the integers and constructing the complete first few
terms of "sigma(n)/n is a power of a rational number that is at least a

Willliam Keith

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