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 A117369 #17 Feb 18 2018 15:31:22
%S A117369 2,3,5,3,7,5,11,3,5,3,13,5,17,3,7,3,19,5,23,3,5,3,29,5,7,3,5,3,31,7,
%T A117369 37,3,5,3,11,5,41,3,5,3,43,5,47,3,7,3,53,5,11,3,5,3,59,5,7,3,5,3,61,7,
%U A117369 67,3,5,3,7,5,71,3,5,3,73,5,79,3,7
%N A117369 a(n) = smallest prime which is > smallest prime dividing n and is coprime to n.
%H A117369 Harvey P. Dale, <a href="/A117369/b117369.txt">Table of n, a(n) for n = 1..1000</a>
%e A117369 a(6) = 5 because 5 is the smallest prime which is both greater than the smallest prime dividing 6, which is 2 and is coprime to 6.
%t A117369 a[1] := 2; a[n_] := Module[{}, k = PrimePi[FactorInteger[n][[1, 1]]]; k++; While[Not[GCD[Prime[k], n] == 1 ], k++ ]; Prime[k]]; Table[a[i], {i, 1, 80}] (* _Stefan Steinerberger_ and Patrick Hanslmaier, Jun 03 2007 *)
%t A117369 spdn[n_]:=Module[{s=FactorInteger[n][[1,1]],p},p=NextPrime[s];While[ !CoprimeQ[ p,n],p=NextPrime[p]];p]; Array[spdn,80] (* _Harvey P. Dale_, Feb 18 2018 *)
%Y A117369 Cf. A079068, A117367.
%K A117369 nonn
%O A117369 1,1
%A A117369 _Leroy Quet_, Mar 10 2006
%E A117369 More terms from _Stefan Steinerberger_ and Patrick Hanslmaier, Jun 03 2007