A074633 a(n) is the smallest index m such that Sum_{k=2..m} 1/PrimePi(k) >= n, where PrimePi()=A000720().
2, 4, 8, 12, 18, 27, 37, 51, 68, 89, 116, 147, 186, 232, 287, 352, 428, 518, 623, 745, 887, 1050, 1240, 1456, 1704, 1987, 2309, 2674, 3090, 3557, 4087, 4684, 5353, 6105, 6949, 7892, 8944, 10121, 11431, 12885, 14502, 16298, 18286, 20485, 22917, 25607
Offset: 1
Keywords
Examples
a(85) = 927685 because 927686 is the smallest m such that Sum_{k=2..m} 1/PrimePi(k) >= 85.
Programs
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Mathematica
{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}]
Extensions
Edited by Jon E. Schoenfield, Apr 04 2023
Name corrected by Sean A. Irvine, Jan 22 2025