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

2003/11/27 by Aleksandar Ivić
Mathematics · #math.NT #msc:11M26 #msc:11M06

paper · pdf

published as Univ. Beogard. Publ. Elektrotehn. Fak. Ser. Mat. 13(2002), 85-88 · 4 pages

arxiv created 2003/11/27 · arxiv updated 2009/12/01

Abstract

A sharp asymptotic formula for the sum of reciprocals of π(n) is derived, where π(x) is the number of primes not exceeding x. This result improves the previous results of De Koninck--Ivić and L. Panaitopol.

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