We prove a refined asymptotic formula for the number of representations of sufficiently large integer as a sum of a prime and a $k$-free number, $k \geqslant 2$.
"On the sum of a prime and a $k$-free number." Funct. Approx. Comment. Math. 34 19 - 26, 2005. https://doi.org/10.7169/facm/1538186584