Let
be the sum of
the divisors of
.
Although much attention has been paid to the possible values of
(the sum
of proper divisors), comparatively little work has been done on the possible values of
. Here we
present some theoretical and computational results on these values. In particular, we
exhibit some infinite and possibly infinite families of integers that appear in the image of
. We also find
computationally all values of
for which
is odd, and we present some data from our computations. At the end of
this paper, we present some conjectures suggested by our computational
work.
Keywords
sigma function, sum of divisors, excedents, computational
mathematics
