[seqfan] A slightly puzzling behavior

[Giovanni Resta]

Hi all,
I've computed the primitive abundant numbers (definition 
https://oeis.org/A091191 ) up to 10^11 and I've
computed how many of them are divisible by the primes 2, 3, 5,... 71.

As expected, most of them are divisible by 2 and/or 3.

However I cannot focus on the reason why an apparently
anomalous fraction of them is divisible by 7 or 31
(both primes of the form 2^k-1). Probably it is obvious,
but right now I cannot see it.

A graph is available here (the last one):
http://www.numbersaplenty.com/set/primitive_abundant/

(note that the similar graph, made for abundant numbers, is
much more regular, showing no peak for 7 or 31).

Any idea?
Giovanni