Abstract
Over the (1, n)-dimensional real superspace, we consider the Lie superalgebra K(n) of contact vector fields on R-1 vertical bar n. We classify osp(n vertical bar 2)-invariant linear differential operators acting on the superspaces of weighted densities. This result allows us to compute the first differential cohomology of K(n) with coefficients in the superspace of weighted densities, vanishing on the Lie superalgebra osp(n vertical bar 2). We explicitly give 1-cocycles spanning these cohomology spaces.