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 A121755 #7 Dec 29 2012 12:25:41
%S A121755 1,5,1,17,2,41,29,1,10,43,16,197,1,281,4,127,4,167,284,3,356,113,1,
%T A121755 321,2,9,8,457,4,9,4,617,2,709,1138,809,4,1,1,147,1,1149,1,1277,2,
%U A121755 1409,317,1,4,1,5,81,1,2027,3169,1,1,1,3709,7699,307,1655,613,8893,4603,1,379,1
%N A121755 Numerator of Sum/Product of first n primes = Numerator[ A007504[n] / A002110[n] ].
%C A121755 Many a(n) are equal to 1. The indices n such that a(n) = 1 are listed in A051838[n] = {1,3,8,13,23,38,39,41,43,48,50,53,56,57,58,66,68,70,73,77,84,90,94,98,...}. Primes p such that a(p) = 1 are listed in A121756[n] = {3,13,23,41,43,53,73,149,151,157,167,191,229,269,293,373,521,557,569,607,691, 701,829,853,863,887,947,991,...}. Many a(n) are primes. It appears that all prime a(n) {5,17,2,41,29,43,197,281,127,167,3,113,457,617,709,809,1277,1409,317,2027,307,...} and all prime divisors of composite a(n) {2,5,71,89,3,107,569,7,383,331,457,...} belong to A111267[n].
%H A121755 Harvey P. Dale, <a href="/A121755/b121755.txt">Table of n, a(n) for n = 1..10000</a>
%F A121755 a(n) = Numerator[ Sum[ Prime[k], {k,1,n} ] / Product[ Prime[k], {k,1,n}] ]. a(n) = Numerator[ A007504[n] / A002110[n] ].
%t A121755 Table[Numerator[Sum[Prime[k],{k,1,n}]/Product[Prime[k],{k,1,n}]],{n,1,100}]
%t A121755 Module[{prs=Prime[Range[70]]},Flatten[Numerator[Thread[ {Accumulate[ prs]/ Rest[ FoldList[Times,1,prs]]}]]]] (* This is several hundred times faster than the first Mathematica program in generating 5000 terms of the sequence *) (* _Harvey P. Dale_, Dec 29 2012 *)
%Y A121755 Cf. A007504, A002110, A121744, A051838, A121756, A120291, A111267.
%K A121755 frac,nonn
%O A121755 1,2
%A A121755 _Alexander Adamchuk_, Aug 19 2006