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A comment on Is the room open?. Parent comment

Re:Is the room open? by jerome-jh on Tuesday February 11, 2020 @11:38AM (#22299801)
perfect square => even number of factors

n = r^2

n = (p1^k1 * p2^k2 * ... * pi^ki)^2

n = p1^(2 * k1) * p2^(2 * k2) * ... * pi^(2 * ki)

hence n has 2 * (k1+k2+...+ki) factors. Or am I wrong?

Reciprocal left as an exercise ;)

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Re:Is the room open? by boyobo on Tuesday February 11, 2020 @04:04PM (#22302830)
Not really sure what your argument is. But it’s wrong, because n=4 is a counterexample. The factors are 1,2 and 4. This is an odd number of factors.

Edit: it seems you are talking about 'The number of factors in the prime factorization of n'. This is not really relevant to the question posed in the submission.

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Re:Is the room open? by jerome-jh on Wednesday February 12, 2020 @08:23AM (#22308565)
Indeed I was talking about prime factors. I understood your point later last night and it is certainly valid. I quite do not understand the original paper though.
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