  We consider K3 surfaces of Picard rank 14 which admit a purely nonsymplectic
automorphism of order 16. The automorphism acts on the second cohomology group
with integer coefficients and we compute the invariant sublattice for the
action. We show that all of these K3 surfaces admit an elliptic fibration and
we compute the invariant lattices in a geometric way by using special curves of
the elliptic fibration. The computation of these lattices plays an important
role when one wants to study moduli spaces and mirror symmetry for lattice
polarized K3 surfaces.
