Above image is taken from Selberg's paper on Elementary proof of prime number theorem. I couldn't apply partial summation formula to get this form. I think first we have to complete the two summations above to include all naturals less than $x$, not only those which are product of two primes. But I couldn't proceed then. Please help.
2026-03-25 20:16:43.1774469803
How do we get this by partial summation formula?
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