Can a Number Have Over 2017 Divisors Within a Specific Range?

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The discussion centers on proving the existence of a natural number \( n \) that has more than 2017 divisors \( d \) within the range \( \sqrt{n} \le d < 1.01 \cdot \sqrt{n} \). Participants emphasize the importance of sharing progress to facilitate effective assistance. The mathematical concepts involved include divisor functions and properties of natural numbers, which are crucial for solving the posed problem.

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anre
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Hello
could you help me to solve my task

$n \in \Bbb{N}$
Prove that there is n which has more than 2017 divisors d that:

$\sqrt{n} \le d < 1,01 * \sqrt{n}$

Thank you
 
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Hello anre and welcome to MHB! :D

We ask that our users show their progress (work thus far or thoughts on how to begin) when posting questions. This way our helpers can see where you are stuck or may be going astray and will be able to post the best help possible without potentially making a suggestion which you have already tried, which would waste your time and that of the helper.

Can you post what you have done so far?
 

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