We establish a Liouville-type theorem for nonnegative weak supersolutions to a nonlocal semilinear equation in the whole Euclidean space. The leading operator is a translation-invariant integro-differential operator of fractional order strictly between zero and two, with an even kernel satisfying uniform ellipticity bounds. We show that the only nonnegative supersolution is the trivial one in the superlinear regime up to the critical Sobolev-type exponent. This covers all superlinear powers when the dimension does not exceed the order of the operator. Our proof is elementary, combining a test function method with a dyadic decomposition of the nonlocal tail. In particular, we use neither the maximum principle nor the fundamental solution.