On weakly prime-additive numbers with length $4k+3$ - Fang, Jin-Hui; Xue, Fang-Gang (Comptes Rendus. Mathématique)
If a positive integer $n$ has at least two distinct prime divisors and can be written as $n=p_1^{α _1}+… +p_t^{α _t}$, where $p_1<… 3$. The main result is summarized as follows: for any positive integers $m,t$ with $t\equiv 3 \pmod {4}$ and $t>3$, there exist infinitely many weakly prime-additive numbers $n$ with $m\mid n$ and $n=p_1^{α _1}+… +p_{t}^{α _{t}}$, where $p_1,… ,p_t$ are distinct prime divisors of $n$ and $α _1,… ,α _t$ are positive integers.