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 A348301 #25 Feb 05 2023 17:56:46
%S A348301 -1,-1,1,37,617,10331,205657,4417993,111313529,3451185211,
%T A348301 113456434771,4398448576657,187757129777747,8377806843970331,
%U A348301 406839682998275587,22177392981497097521,1341055344385518798469,83727136357670859345679,5727006517323354547143763
%N A348301 a(n) is the difference between the numerator and denominator of the (reduced) fraction Sum_{i = 1..n} 1/prime(i).
%H A348301 Harvey P. Dale, <a href="/A348301/b348301.txt">Table of n, a(n) for n = 1..350</a>
%F A348301 a(n) = (Sum_{i = 1..n} p_n# / p_i) - p_n# where p_n# is the primorial of the n-th prime.
%F A348301 a(n) = A024451(n) - A002110(n).
%e A348301 a(1) = (p_1# / p_1) - p_1 = (2 / 2) - 2 = -1.
%e A348301 a(2) = (p_2# / p_1 + p_2# * p_2) - p_1 * p_2 = (6 / 2 + 6 / 3) - 2 * 3 = -1.
%e A348301 a(3) = 2*3*5/2 + 2*3*5/3 + 2*3*5/5 - 2*3*5 = 31 - 30 = 1.
%t A348301 Numerator[#]-Denominator[#]&/@Accumulate[1/Prime[Range[20]]] (* _Harvey P. Dale_, Feb 05 2023 *)
%o A348301 (Python)
%o A348301 from itertools import islice
%o A348301 from sympy import primorial, sieve
%o A348301 def a(n): return sum(primorial(n) // p for p in islice(sieve, n)) - primorial(n) # _Greg Tener_, Oct 18 2021
%o A348301 (PARI) a(n) = my(q=sum(i=1, n, 1/prime(i))); numerator(q)-denominator(q); \\ _Michel Marcus_, Oct 18 2021
%Y A348301 Cf. A024451 (numerators), A002110 (denominators).
%K A348301 sign
%O A348301 1,4
%A A348301 _Greg Tener_, Oct 10 2021