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## Main Question or Discussion Point

I have seen double sums, but have come across a problem involving sums over primes. However, this sum is inside a second sum, and is taken over all primes that divide the outside index, like this:

[itex] \sum_{k=1}^{n} \sum_{p | k} \frac 1p [/itex]

for p prime.

Is there any way to manipulate this? Any help would be appreciated.

Thanks!

[itex] \sum_{k=1}^{n} \sum_{p | k} \frac 1p [/itex]

for p prime.

Is there any way to manipulate this? Any help would be appreciated.

Thanks!