$\mathbb{Z}$-coefficients) of the space $\bigvee^{r}_{i = 1} S^{n_{i}} * \bigvee^{s}_{j = 1} S^{m_{j}}$, where $r, s, n_i, m_j \geq 0$ and $*, \vee$ denote the join and wedge sum operations, respectively. I can compute these homology groups of pure wedges sums of spheres or of the pure topological joins of spheres,