Mathematics - Functions Question with Solution | TestHub

A function $f$ is defined as $f(\alpha )=(-1{)}^{{\alpha }_1}+(-1{)}^{{\alpha }_2}+(-1{)}^{{\alpha }_3}+\dots +(-1{)}^{{\alpha }_k}$, where $\alpha \in \mathbb{N}$, and ${\alpha }_1,{\alpha }_2,\dots ,{\alpha }_k$ are all divisors of $\alpha$, including 1 and itself, such that ${\alpha }_1\cdot {\alpha }_2\cdot \dots \cdot {\alpha }_k=\alpha$ and ${\alpha }_1,{\alpha }_2,\dots ,{\alpha }_k\in \mathbb{N}$.

If $f(\alpha )=4$ and $\alpha <60$, then find the number of possible values of $\alpha$.