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A197861 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the smaller prime.

%I A197861 #6 Mar 30 2012 17:35:25
%S A197861 2,3,2,5,3,7,2,3,5,11,2,13,7,5,2,17,3,19,5,7,11,23,3,5,13,3,7,29,2,31,
%T A197861 2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,2,7,5,17,13,53,3,11,7,19,
%U A197861 29,59,2,61,31,3,2,13,11,67,17,23,5,71,3,73,37,5,19
%N A197861 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the smaller prime.
%e A197861 The only prime divisor of 4 is 2, so a(4) = 2.
%e A197861 The prime divisors of 6 are 2 and 3; in the sequence to that point (2,3,2,5), there are two 2's and 1 3, we take the less common one, so a(6) = 3.
%e A197861 The prime divisors of 12 are 2 and 3; these occur equally often in the sequence to that point, so we take the smaller one; a(12)=2.
%o A197861 (PARI) al(n)={local(ns=vector(primepi(n)),r=vector(n-1),ps);
%o A197861   for(k=1,n-1,
%o A197861     ps=factor(k+1)[,1]~;
%o A197861     r[k]=ps[1];
%o A197861     for(j=2,#ps,if(ns[primepi(ps[j])]<ns[primepi(r[k])],r[k]=ps[j]));
%o A197861     ns[primepi(r[k])]++);
%o A197861   r}
%Y A197861 Cf. A197862, A006530.
%K A197861 nonn
%O A197861 2,1
%A A197861 _Franklin T. Adams-Watters_, Oct 18 2011