[seqfan] Re: A294900 Interesting abundant numbers

Giovanni Resta giovanni.resta at iit.cnr.it
Mon Dec 11 15:22:16 CET 2017

On 12/08/2017 12:42 AM, Iain Fox wrote:
> Dear SeqFan members,
> I have been doing some investigating into the sequence, A294900, which contains all numbers such that the sum of its nonabundant divisors is itself. Naturally, this contains all perfect numbers, but I also proved that any non-perfect term is abundant. These abundant numbers would be pseudoperfect (or semiperfect) numbers. Are there any other things that these abundant terms would have in common with each other?

I've added 3 terms: 17589794838, 35439846824, 49380301744.

I've also noticed that the numbers which are the sum of their abundant 
proper divisors seems to be scarcer. Indeed, up to 6*10^10, there are 
only 2 such numbers: 19514300 and 16333377500.


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