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A197862 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the larger prime.

%I A197862 #5 Mar 30 2012 17:35:25
%S A197862 2,3,2,5,3,7,2,3,5,11,3,13,7,5,2,17,3,19,5,7,11,23,2,5,13,3,7,29,5,31,
%T A197862 2,11,17,7,3,37,19,13,5,41,7,43,11,5,23,47,2,7,2,17,13,53,3,11,7,19,
%U A197862 29,59,5,61,31,7,2,13,11,67,17,23,7,71,3,73,37,5,19
%N A197862 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the larger prime.
%C A197862 Up to n = 100, this differs from the greatest prime factor function A006530 only at n = 24, 48, 50, 80, and 98.
%e A197862 The only prime divisor of 4 is 2, so a(4) = 2.
%e A197862 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 A197862 The prime divisors of 12 are 2 and 3; these occur equally often in the sequence to that point, so we take the larger one; a(12)=3.
%o A197862 (PARI) al(n)={local(ns=vector(primepi(n)),r=vector(n-1),ps);
%o A197862   for(k=1,n-1,
%o A197862     ps=factor(k+1)[,1]~;
%o A197862     r[k]=ps[1];
%o A197862     for(j=2,#ps,if(ns[primepi(ps[j])]<=ns[primepi(r[k])],r[k]=ps[j]));
%o A197862     ns[primepi(r[k])]++);
%o A197862   r}
%Y A197862 Cf. A197861, A006530.
%K A197862 nonn
%O A197862 2,1
%A A197862 _Franklin T. Adams-Watters_, Oct 18 2011