I wish the question is clearly explained in the title. Thanks in advance.
2026-03-30 15:15:49.1774883749
How to show that $\sigma(n)=k$ has a finite # of solutions $k\in\mathbb{N}$?
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Since $n$ divides $n$ then $ k=\sigma(n) \ge n. $ Hence there are at most $k$ solutions.