  We re-analyze the production of seed magnetic fields during Inflation in
(R/m^2)^n F_{\mu \nu}F^{\mu \nu} and I F_{\mu \nu}F^{\mu \nu} models, where n
is a positive integer, R the Ricci scalar, m a mass parameter, and I \propto
\eta^\alpha a power-law function of the conformal time \eta, with \alpha a
positive real number. If m is the electron mass, the produced fields are
uninterestingly small for all n. Taking m as a free parameter we find that, for
n \geq 2, the produced magnetic fields can be sufficiently strong in order to
seed dynamo mechanism and then to explain galactic magnetism. For \alpha
\gtrsim 2, there is always a window in the parameters defining Inflation such
that the generated magnetic fields are astrophysically interesting. Moreover,
if Inflation is (almost) de Sitter and the produced fields almost
scale-invariant (\alpha \simeq 4), their intensity can be strong enough to
directly explain the presence of microgauss galactic magnetic fields.
