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Question Number 217198 by hardmath last updated on 05/Mar/25

Answered by MrGaster last updated on 05/Mar/25

$$\delta \left(n\right)=\sum _{d\mid n}d,‘‘\tau \left(n\right)=\sum _{d\mid n}\cancel{l}\stackrel{\left(\mathrm{Unknown}\mathrm{meaning}\right)}{\Rightarrow }{1}^{″}\mathrm{and}\phi -{\mathrm{Euler}}^{,}\mathrm{s}\mathrm{totient}\mathrm{function}$$$$\delta \left(n\right)=\underset{i=1}{\prod ^k}(p_i^{a_i+1}+1)/(p_i-1)$$$$\mathrm{where}n=\underset{i=1}{\prod ^k}(a_i+1)$$$$\phi \left(n\right)=n\underset{i=1}{\prod ^k}(1-\frac{1}{p_i})$$$$\Rightarrow \delta \left(n\right)=\sum _{d\mid n}\phi \left(d\right)\tau \left(\frac{n}{d}\right)=\underset{i=1}{\prod ^k}(p_i^{a_i+1}-1)/(p_i-1)$$$$[Q.\mathrm{E}.\mathrm{D}]$$

Commented by hardmath last updated on 16/Mar/25

$$\mathrm{thankyou}\mathrm{dear}\mathrm{professor}$$

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