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 A354859 #7 Jun 09 2022 17:18:40
%S A354859 1,4,71,124,11111,92402,257189,43708274,2344987003,1855369084,
%T A354859 2729707472269,11281836318542,1705853427969059,120757830191824486,
%U A354859 1124815045783478971,118422287191742563724,1291008724583331399881,113743044027018860349034,70575236921156825443680027,8002471039307070610187173702
%N A354859 a(n) is the numerator of 1/prime(n) + 2/prime(n-1) + 3/prime(n-2) + ... + (n-1)/3 + n/2.
%C A354859 Numerator of a second order prime harmonic number.
%F A354859 a(n) is the numerator of Sum_{j=1..n} Sum_{i=1..j} 1/prime(i).
%e A354859 1/2, 4/3, 71/30, 124/35, 11111/2310, 92402/15015, 257189/34034, ...
%t A354859 Table[Sum[(n - k + 1)/Prime[k], {k, 1, n}], {n, 1, 20}] // Numerator
%o A354859 (Python)
%o A354859 from fractions import Fraction
%o A354859 from sympy import prime, primerange
%o A354859 def a(n): return sum(Fraction(n-i, p) for i, p in enumerate(primerange(1, prime(n)+1))).numerator
%o A354859 print([a(n) for n in range(1, 21)]) # _Michael S. Branicky_, Jun 09 2022
%Y A354859 Cf. A024451, A027612, A120272, A354860 (denominators).
%K A354859 nonn,frac
%O A354859 1,2
%A A354859 _Ilya Gutkovskiy_, Jun 09 2022