Perfect Abs

[Hans Havermann]

On January 13, Ed Pegg Jr. submitted A101367 and A101366 (both of which 
I extended today). On the same day, T.D. Noe submitted A102531 and 
A102532, which appear (on the surface) to be be Ed's two sequences with 
the added inclusion of the known real perfects {6, 28, 496,...}.

Unfortunately, they use different Mathematica functions to determine 
the sequences and while I don't understand why the Mathematica 
functions should provide differing results in their application to 
complex numbers, it appears they do:

DivisorSigma[1, 5 + 3 I] = 10 I
Total[Divisors[5 + 3 I]] = 8 + 8 I

and, as a result, (5 + 3 I) will appear in Ed's but not in Noe's 
sequences.

For the same reason, (472 + 664 I) is a solution to Noe's sequences, 
but not in Ed's. Perversely, (827 + 664 I) is a solution in Ed's 
sequences, but not in Noe's.

Anyways, just thought I'd bring this to everyone's attention in the 
hopes of clarifying the definitional aspects of these sequences.

Hans