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 A347310 a(n) = smallest k such that Sum_{i=1..k} log(p_i)/p_i >= n, where p_i is the i-th prime. 1
 3, 8, 19, 43, 100, 236, 562, 1354, 3300, 8119, 20136, 50302, 126451, 319628, 811829, 2070790, 5302162, 13621745, 35101258, 90696900, 234924747, 609864582, 1586430423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suggested by Mertens's theorem that Sum_{p <= x} log(p)/p = log(x) + O(1). REFERENCES Tenenbaum, G. (2015). Introduction to analytic and probabilistic number theory, 3rd ed., American Mathematical Soc. See page 16. LINKS Table of n, a(n) for n=1..23. FORMULA a(n) = pi(A347311(n)) = A000720(A347311(n)). - Michel Marcus, Sep 06 2021 EXAMPLE a(1) = 3 because log(2)/2 + log(3)/3 + log(5)/5 = 1.034665268989... is the first time the sum is >= 1. MATHEMATICA Table[k=1; While[Sum[Log@Prime@i/Prime@i, {i, ++k}]

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Last modified April 18 03:33 EDT 2024. Contains 371767 sequences. (Running on oeis4.)