This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120055 #23 Mar 27 2021 07:47:48
%S A120055 4,35,871,43217,5296623,2011783478
%N A120055 a(n) is the least semiprime s such that the Sum_{semiprime i <= s} 1/i exceeds n.
%C A120055 A002387(n+1) < a(n) < A016088(n).
%C A120055 a(n) is the k-th semiprime: k = 1, 13, 262, 10521, 1034924, 316108902; factors: 2*2, 5*7, 13*61, 23*1879, 3*1765541, 2*1005891739.
%C A120055 For a(1), sum = 1.025694370988488635...
%C A120055 for a(2), sum = 2.000920208207319042...
%C A120055 for a(3), sum = 3.000000294546501318...
%C A120055 for a(4), sum = 4.000000031685702432...
%C A120055 for a(5), sum = 5.000000000169814007...
%e A120055 a(0)=4 because 1/4 > 0.
%e A120055 a(1)=35 because 1/4 + 1/6 + 1/9 + 1/10 + 1/14 + 1/15 + 1/21 + 1/22 + 1/25 + 1/26 + 1/33 + 1/34 + 1/35 = 15708817/15315300 > 1.
%t A120055 s = 0; k = 1; Do[ While[s <= n, If[ Plus @@ Last /@ FactorInteger@k == 2, s = N[ s + 1/k, 20]]; k++ ]; Print[{k - 1, s}]; k ++, {n, 0, 5}]
%Y A120055 Cf. A002387, A016088.
%K A120055 nonn,more
%O A120055 0,1
%A A120055 _Jonathan Vos Post_ and _Robert G. Wilson v_, Mar 25 2006