COMMENT on A064161

Dean Hickerson dean at
Fri Mar 28 05:59:45 CET 2003

Neil:  As Jose Brox pointed out, the Mathematica code could be made more
efficient in A064161. Please change this:

%t A064161 a[n_]:=For[k=1,True,k++,If[DivisorSigma[ -1,t=k*Prime[n]]>2,Return[t]]]

to this:

%t A064161 If[n==2||n==3,4,6]Prime[n]

Jose:  I'm the one who edited the sequence to include your observation.
I wrote the first program above as a test, and didn't bother to replace it
by a more efficient one after confirming that your theorem was correct.
Thanks for the suggestion.

You also asked:

> Should we add the proof?

I don't think it's necessary.  It's pretty straightforward to check that
p, 2p, 3p, 4p, and 5p are not abundant if p>=7.

Dean Hickerson
dean at

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