I forgot a requirement in my previous question (Find me 5 special squares) I am afraid now that this one is too simple/similar, but this was what I actually intended:

There are many squares that cannot be written as a number divided by the number of prime factors of that number.

Can you give me 5 of such squares that both
1 are relatively prime
2 can be divided by their number of prime factors

(Example: 16 is no such square since sqr(4)*6 has 6 prime factors)
(Example: 2^14 is no such square since it is not divisible by 14)


Nope. When counting prime factors with multiplicities square numbers will have an even count. Hence every very special square must be even, so any two of them cannot be relatively prime.

  • $\begingroup$ hm. I should learn to ask good questions, feel ashamed that it is even simpler than anticipated. $\endgroup$ – Retudin Sep 11 '20 at 5:42
  • 1
    $\begingroup$ @Retudin don't beat yourself up about it ;-) $\endgroup$ – Paul Panzer Sep 11 '20 at 6:31

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