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a(n) is the smallest index m such that Sum_{k=1..m} 1/PrimePi(k) >= n, where PrimePi()=A000720().
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%I #9 Apr 05 2023 08:28:12

%S 2,4,8,12,18,27,37,51,68,89,116,147,186,232,287,352,428,518,623,745,

%T 887,1050,1240,1456,1704,1987,2309,2674,3090,3557,4087,4684,5353,6105,

%U 6949,7892,8944,10121,11431,12885,14502,16298,18286,20485,22917,25607

%N a(n) is the smallest index m such that Sum_{k=1..m} 1/PrimePi(k) >= n, where PrimePi()=A000720().

%e a(85) = 927685 because 927686 is the smallest m such that Sum_{k=1..m} 1/PrimePi(k) >= 85.

%t {s=0, s1=0}; Do[s=s+(1/PrimePi[n]); If[Greater[Floor[s], s1], s1=Floor[s]; Print[{n, Floor[s]}]], {n, 2, 1000000}]

%Y Cf. A004080, A046024, A074631, A000720.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 28 2002

%E Edited by _Jon E. Schoenfield_, Apr 04 2023