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Let $d_1, d_2,..., d_k$ be all factors oc a positive integer $n$ including 1 and n. Suppose $d_1+d_2+... +d_k=72$. The question is to evaluate $$\sum_{i=1}^k \frac1d_i$$

I found this question in Test of Maths at 10+2level. I tried applying inequality which made it ascertain that the summation is greater than $72/k$ but i couldn't find it's value. Any ideas? Thanks. .

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Since $71$ is prime, $k=2$ is certainly a possibility, so ${72\over 71}$ seems a reasonable response to this question.

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