On a sum involving the prime counting function π(x)
classification
🧮 math.NT
keywords
asymptoticcountingderivedexceedingformulafunctionimprovesinvolving
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A sharp asymptotic formula for the sum of reciprocals of $\pi(n)$ is derived, where $\pi(x)$ is the number of primes not exceeding $x$. This result improves the previous results of De Koninck--Ivi\'c and L. Panaitopol.
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