%I #12 Nov 29 2020 05:37:32
%S 1,1,2,1,3,1,5,1,1,1,1,1,1,11,1,1,19,23,1,1,1,89,13,61,71,1,1,37,1,1,
%T 17,1,7,1,1,167,1,1,491,53,1,31,1,227,1,1,1,97,1,59,241,29,1,953,1063,
%U 1777,1,367,1,1
%N Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009.
%C Conjecture: a(n) > 1 for all n > 203.
%H Zhi-Wei Sun, <a href="/A242180/b242180.txt">Table of n, a(n) for n = 1..6000</a>
%e a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5).
%e a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2.
%t f[n_]:=FactorInteger[PartitionsQ[n]]
%t pp[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]
%t Do[If[PartitionsQ[n]<2,Goto[cc]];Do[Do[If[Mod[PartitionsQ[i],Part[pp[n],k]]==0,Goto[aa]],{i,1,n-1}];Print[n," ",Part[pp[n],k]];Goto[bb];Label[aa];Continue,{k,1,Length[pp[n]]}];Label[cc];Print[n," ",1];Label[bb];Continue,{n,1,60}]
%Y Cf. A000009, A000040, A084911, A194261, A272170, A272171, A272173.
%K nonn
%O 1,3
%A _Zhi-Wei Sun_, May 06 2014