[seqfan] Re: A335071 question.

hv at crypt.org hv at crypt.org
Sat May 30 20:05:13 CEST 2020

michel.marcus at free.fr wrote:
:In A335071, there is a question: Can two consecutive numbers have the same
:abundancy: sigma(m)/m = sigma(m+1)/(m+1)? 
:Do you have an idea ? 

We need sigma(m) = km, sigma(m+1) = k(m+1) for some integer k, so any
such pair of numbers would have to be a consecutive pair in A007691.
Given the rate of growth (and lack of odd numbers) there, it seems
exceedingly unlikely.

Do we even know an example of an odd entry > 1? None appears in the
table of the first 1600 values, which ends with a 304-digit number,
and finding one seems barely more likely than finding an odd perfect

Hugo van der Sanden

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