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Question Number 174522 by Mastermind last updated on 03/Aug/22

$$\mathrm{Let}\sigma \left(\mathrm{n}\right)\mathrm{be}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{all}\mathrm{positive}\mathrm{divisors}$$ $$\mathrm{of}\mathrm{the}\mathrm{integer}\mathrm{n}\mathrm{and}\mathrm{let}\mathrm{p}\mathrm{be}\mathrm{any}\mathrm{prime}$$ $$\mathrm{number}.\mathrm{Show}\mathrm{that}\sigma \left(\mathrm{n}\right)<2\mathrm{n}\mathrm{holds}\mathrm{true}$$ $$\mathrm{for}\mathrm{all}\mathrm{n}\mathrm{of}\mathrm{the}\mathrm{form}\mathrm{n}={\mathrm{p}}^2.$$ $$$$ $$\mathrm{Mastermind}$$

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