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Question Number 183998 by JDamian last updated on 01/Jan/23

Find the natural number n such         n=7^a ∙17^b       a∈N,   b∈N  and the sum of all its divisors (1 and  n included) is 2456.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\boldsymbol{\mathrm{n}}\:{such} \\ $$$$\:\:\:\:\:\:\:{n}=\mathrm{7}^{{a}} \centerdot\mathrm{17}^{{b}} \:\:\:\:\:\:{a}\in\mathbb{N},\:\:\:{b}\in\mathbb{N} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{its}\:\mathrm{divisors}\:\left(\mathrm{1}\:\mathrm{and}\right. \\ $$$$\left.\boldsymbol{\mathrm{n}}\:\mathrm{included}\right)\:\mathrm{is}\:\mathrm{2456}. \\ $$

Commented by Rasheed.Sindhi last updated on 01/Jan/23

          determinant (((n=2023=7^1 ∙17^2 )))  ★_★ ^★ Happy New Year_★ ^★ ★_(−) ^(−)

$$\:\:\:\:\:\:\:\:\:\begin{array}{|c|}{\boldsymbol{\mathrm{n}}=\mathrm{2023}=\mathrm{7}^{\mathrm{1}} \centerdot\mathrm{17}^{\mathrm{2}} }\\\hline\end{array} \\ $$$$\underset{−} {\overline {\bigstar_{\bigstar} ^{\bigstar} \boldsymbol{\mathrm{Happy}}\:\boldsymbol{\mathrm{New}}\:\boldsymbol{\mathrm{Year}}_{\bigstar} ^{\bigstar} \bigstar}} \\ $$

Answered by Rasheed.Sindhi last updated on 01/Jan/23

            determinant (((n=2023=7^1 ∙17^2 _( SumOfDivisors_(1+7+17+119+289+2023_(=2456) ) ) )))

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\begin{array}{|c|}{\underset{\underset{\underset{=\mathrm{2456}} {\mathrm{1}+\mathrm{7}+\mathrm{17}+\mathrm{119}+\mathrm{289}+\mathrm{2023}}} {\:\boldsymbol{\mathcal{S}{um}\mathcal{O}{f}\mathcal{D}}{ivisors}}} {\boldsymbol{\mathrm{n}}=\mathrm{2023}=\mathrm{7}^{\mathrm{1}} \centerdot\mathrm{17}^{\mathrm{2}} }}\\\hline\end{array} \\ $$$$ \\ $$

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