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How to find the number $P$ of integers $(n,m)$ such that $\operatorname{lcm}(n,m) = k$? Only $k$ is given.

I only find the number of $n$ such that $\operatorname{lcm}(n,k) = k$.

Can anyone help me solve this problem?

Thanks.

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    Are you asking to find the number P of pairs $(n,m)$ such that $k=lcm(n,m)$ for a given $k$?2012-04-30
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    One could do worse than to write the decomposition of `k` as a product of powers of primes and to wonder what the decompositions of the integers `n` and `m` can be.2012-04-30
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    @GiovanniDeGaetano yes I'm asking that.2012-04-30
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    @Didier: I would call that a good hint and answer2012-04-30
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    @Ross Thanks. Done.2012-04-30
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    Start modestly, how many pairs have lcm $7$? What about $4$? $8$? $24$? After a while you will know exactly what's going on. Then the symbols stuff will be easy.2012-04-30
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    Elmi: Any luck with the answer below?2012-05-07

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