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ParthKohli

  • 2 years ago

The least positive number such that the number of divisors of the number of divisors of the number of divisors of the number of divisors of the original number is \(3\).

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  1. ParthKohli
    • 2 years ago
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    Now, I get \(72\) which is apparently wrong by doing repeated backward-working. ``` 72 => 1,2,3,4,6,8,9,12,24,36,72 | | V 12 => 1,2,3,4,6,12 | | V 6 => 1,2,3,6 | | V 4 => 1,2,4 | | V 3 ```

  2. ParthKohli
    • 2 years ago
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    So is there a number smaller than \(72\) which satisfies the conditions?

  3. shubhamsrg
    • 2 years ago
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    60 ?

  4. ParthKohli
    • 2 years ago
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    ``` 60 = 2^2 * 3 * 5 | | V 12 | | V . . . ``` OMG, so 60 is the answer?!

  5. ParthKohli
    • 2 years ago
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    I get how you did the last step by doing \(12 = 2 \cdot 2 \cdot 3\ \) :-) I did the rest of the steps just like that!

  6. ParthKohli
    • 2 years ago
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    Is \(60\) it?

  7. ParthKohli
    • 2 years ago
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    I think it is.

  8. shubhamsrg
    • 2 years ago
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    60 is the least number with 12 divisors, I'll tell you how I remembered that. Gimme a min.

  9. ParthKohli
    • 2 years ago
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    No, I know the divisor function. I was just doing least numbers throughout :-)

  10. shubhamsrg
    • 2 years ago
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    hmm.

  11. ParthKohli
    • 2 years ago
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    For example, take \(2^2 3^1\). This number has \((2 + 1)(1 + 1) = 6\) divisors.

  12. ParthKohli
    • 2 years ago
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    And to find the least number, you first prime factorize the number, then adjust the powers such that the least prime number gets the highest power and so on.

  13. ParthKohli
    • 2 years ago
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    \[6 = 2\cdot 3 = 3\cdot 2 =6\cdot 1 =1 \cdot 6\]Now we can kinda see that it's evident how \(2^2 3^1\) is the least number. :-)

  14. ParthKohli
    • 2 years ago
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    I couldn't realize that we could take a product of three primes too :-)

  15. ParthKohli
    • 2 years ago
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    Do you know how divisor function works?

  16. shubhamsrg
    • 2 years ago
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    I had seen a very similar question on OS long time ago. That is how I could instantly say 60 ! :P Nevermind, I follow your reasoning very well. Kudos! B|

  17. ParthKohli
    • 2 years ago
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    L O L

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