Asymptotics of the counting function of $k$-th power-free elements in an arithmetic semigroup

V. L. Chernyshev, D. S. Minenkov, V. E. Nazaikinskii

For any $k>1$, we find the asymptotics of the counting function of $k$-th power-free elements in an additive arithmetic semigroup with exponential growth of the abstract prime coun…