On a sum involving the prime counting function $π(x)$

Details On a sum involving the prime counting function $π(x)$ On a sum involving the prime counting function $π(x)$

2003-11-27

arxiv.org/abs/math/0311498v1

Univ. Beogard. Publ. Elektrotehn. Fak. Ser. Mat. 13(2002), 85-88

Mathematics

Number Theory

4 pages

Scientific paper

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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