A Romanoff-type theorem for $P_2$+{$a^a$: a$\ge$ 1}

Yuchen Ding, Huixi Li, Junfeng Li

Let $\hat{I}\text{c◯}(n)$ denote the number of prime factors of $n$, counted with multiplicity, and put $P_2$={$m$ $\ge$ 1:$\hat{I}\text{c◯}(m)$ $\le$ 2}. We prove that the sumset $P_2$+{$a^a$: a$\ge$ 1} has…