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ParthKohli

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 \(3\).

  • one year ago
  • one year ago

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  1. ParthKohli
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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 ```

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

    • one year ago
  3. shubhamsrg
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    60 ?

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

    • one year ago
  5. ParthKohli
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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!

    • one year ago
  6. ParthKohli
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    Is \(60\) it?

    • one year ago
  7. ParthKohli
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    I think it is.

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

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

    • one year ago
  10. shubhamsrg
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    hmm.

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

    • one year ago
  12. ParthKohli
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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.

    • one year ago
  13. ParthKohli
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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. :-)

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

    • one year ago
  15. ParthKohli
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    Do you know how divisor function works?

    • one year ago
  16. shubhamsrg
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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|

    • one year ago
  17. ParthKohli
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    L O L

    • one year ago
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