Let-n-be-the-sum-of-all-positive-divisors-of-the-integer-n-and-let-p-be-any-prime-number-Show-that-n-lt-2n-holds-true-for-all-n-of-the-form-n-p-2-Mastermind-

Tinku Tara June 4, 2023 Others 0 Comments

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

Let σ(n) be the sum of all positive divisors of the integer n and let p be any prime number. Show that σ(n)<2n holds true for all n of the form n=p^2 . Mastermind

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

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Let-n-be-the-sum-of-all-positive-divisors-of-the-integer-n-and-let-p-be-any-prime-number-Show-that-n-lt-2n-holds-true-for-all-n-of-the-form-n-p-2-Mastermind-

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