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 A120271 #31 May 03 2025 17:00:10
%S A120271 1,3,7,23,121,21,173,1597,17927,127469,129317,43619,44081,44521,
%T A120271 1033223,13538159,395369371,132680013,400467919,402757063,1214947859,
%U A120271 1221110939,50305908619,50529880549,101470376303,509322834499,8691337402883
%N A120271 a(n) = numerator(Sum_{k=1..n} 1/(prime(k)-1)).
%C A120271 a(n) is squarefree except for n = 5, 14, 49, ... where squared prime factors are 11, 211, 479, ...
%C A120271 a(n)/A128646(n) is the asymptotic mean over the positive integers of the number of prime divisors that are not greater than prime(n), counted with multiplicity (cf. A007814, A169611, A356006). - _Amiram Eldar_, Jul 23 2022
%H A120271 Robert Israel, <a href="/A120271/b120271.txt">Table of n, a(n) for n = 1..1495</a>
%H A120271 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>.
%F A120271 a(n) = numerator(Sum_{k=1..n} 1/(prime(k)-1)).
%F A120271 a(n) = A078456(n) * A135212(n). - _Alexander Adamchuk_, Nov 23 2007
%p A120271 R:= [seq(1/(ithprime(k)-1),k=1..40)]:
%p A120271 S:= ListTools:-PartialSums(R):
%p A120271 A:= map(numer,S); # _Robert Israel_, Jan 12 2025
%t A120271 Numerator[Table[Sum[1/(Prime[i]-1),{i,1,n}],{n,1,50}]]
%t A120271 Accumulate[1/(Prime[Range[30]]-1)]//Numerator (* _Harvey P. Dale_, May 03 2025 *)
%o A120271 (PARI) a(n) = numerator(sum(k=1, n, 1/(prime(k)-1))); \\ _Michel Marcus_, Oct 02 2016
%Y A120271 Cf. A128646 (denominators), A119686, A006093, A000040.
%Y A120271 Cf. A135212, A078456.
%Y A120271 Cf. A007814, A169611, A356006.
%K A120271 frac,nonn
%O A120271 1,2
%A A120271 _Alexander Adamchuk_, Jul 01 2006