We develop an analytic integral equation theory for treating polymer-induced effects on the structure and thermodynamics of dilute suspensions of hard spheres. Results are presented for the potential of mean force, free energy of insertion per particle into a polymer solution, and the second virial coefficient between spheres. The theory makes predictions for all size ratios between the spheres and the polymer coil dimension. Based on the Percus-Yevick (PY) closure, the attractive polymer-induced depletion interaction is predicted to be too weak under athermal conditions to induce a negative value for the second virial coefficient, B-2(cc), between spheres in the colloidal limit when the spheres are much larger than the coil size. A nonmonotonic dependence of the second virial coefficient on polymer concentration occurs for small enough particles, with the largest polymer-mediated attractions and most negative BSC occurring near the dilute-semidilute crossover concentration. Predictions for the polymer-mediated force between spheres are compared to the results of computer simulations and scaling theory.