Abstract
Let \({\pi(x)}\) be the number of primes not exceeding x. We produce new explicit bounds for \({\pi(x)}\) and we use them to obtain a fine frame for the remainder term in the asymptotic formula of the sum \({\sum_{2\leq n\leq x}1/\pi(n)}\).
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To the memory of Laurenţiu Panaitopol.
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Berkane, D., Dusart, P. On a Constant Related to the Prime Counting Function. Mediterr. J. Math. 13, 929–938 (2016). https://doi.org/10.1007/s00009-015-0564-9
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DOI: https://doi.org/10.1007/s00009-015-0564-9