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 A120272 #22 Sep 08 2022 08:45:25
%S A120272 0,1,7,53,491,6451,97723,1871501,39642599,999076987,31204161323,
%T A120272 1038495626543,40831064063651,1770543222362221,80392862250956443,
%U A120272 3974705945770003271,220497651647226035923,13563377141298566879867,861975691921988407175147,59980850604601955729416979
%N A120272 Numerator of Sum_{k=1..n} k/prime(k).
%H A120272 Harvey P. Dale, <a href="/A120272/b120272.txt">Table of n, a(n) for n = 0..349</a>
%F A120272 a(n) = A258851(A002110(n)). - _Alois P. Heinz_, Jun 26 2015
%t A120272 Numerator[Table[Sum[i/Prime[i],{i,1,n}],{n,1,20}]]
%t A120272 Numerator[Accumulate[Table[n/Prime[n],{n,20}]]] (* _Harvey P. Dale_, Jan 21 2013 *)
%o A120272 (PARI) for(n=0,20, print1(if(n==0, 0, numerator(sum(k=1,n, k/prime(k)))), ", ")) \\ _G. C. Greubel_, Aug 23 2018
%o A120272 (Magma) [0] cat [Numerator((&+[k/NthPrime(k): k in [1..n]])): n in [1..20]]; // _G. C. Greubel_, Aug 23 2018
%Y A120272 Denominators are in A002110.
%K A120272 frac,nonn
%O A120272 0,3
%A A120272 _Alexander Adamchuk_, Jul 01 2006
%E A120272 a(0)=0 prepended by _Alois P. Heinz_, Jun 26 2015