--- In

primenumbers@yahoogroups.com, "leavemsg1" wrote:

> >

> > > sigma(n^2) > (n+1)(n-1)= n^2 -1; taking

> > > sigma again leads to... sigma(sigma(n^2)) > sigma(n^2 -1);

> >

> > sigma isn't increasing

>

> the sigma function itself varies...

nice start.

> but sigma(sigma(n^2)) isn't ever larger than sig(n^2 -1);

forstep(n=3,99,2, sigma(sigma(n^2))>sigma(n^2-1) & print("Yes it is, for n=",n))

Yes it is, for n=21

Yes it is, for n=63

Yes it is, for n=75

Yes it is, for n=93

> oh well... in for a penny, in for a pound; my chess champion friend

> said it would probably fall on deaf ears.

unfortunately not, but I'll soon go thru the effort of the 3 clicks needed on gmail to filter "leavemsg1" directly into the Trash folder.

M.