On the sum of a prime and a number that is not square-free

We prove that every sufficiently large integer n can be written as the sum of a prime and an integer that is not square-free. In addition, we expect this result holds for every $$n > 24$$ n > 24 and prove two results to support this claim. First, we prove the result holds unconditionally for every odd $$n > 24$$ n > 24 . Second, assuming the Generalised Riemann Hypothesis for Dirichlet L -functions, we prove the result holds for every $$n > 24$$ n > 24 . We also discuss the obstruction which prohibits us from proving the result unconditionally for every $$n > 24$$ n > 24 .