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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)

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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.

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  • $\begingroup$ 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
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    $\begingroup$ @Retudin don't beat yourself up about it ;-) $\endgroup$ – Paul Panzer Sep 11 '20 at 6:31

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