%I
%S 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 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 67,3,5,3,7,5,71,3,5,3,73,5,79,3,7
%N a(n) = smallest prime which is > smallest prime dividing n and is coprime to n.
%H Harvey P. Dale, <a href="/A117369/b117369.txt">Table of n, a(n) for n = 1..1000</a>
%e 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 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 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 Cf. A079068, A117367.
%K nonn
%O 1,1
%A _Leroy Quet_, Mar 10 2006
%E More terms from _Stefan Steinerberger_ and Patrick Hanslmaier, Jun 03 2007
