%I
%S 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 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 29,59,5,61,31,7,2,13,11,67,17,23,7,71,3,73,37,5,19
%N Prime divisor of n which appears the fewest times previously in the sequence, with ties to the larger prime.
%C Up to n = 100, this differs from the greatest prime factor function A006530 only at n = 24, 48, 50, 80, and 98.
%e The only prime divisor of 4 is 2, so a(4) = 2.
%e 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 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 (PARI) al(n)={local(ns=vector(primepi(n)),r=vector(n1),ps);
%o for(k=1,n1,
%o ps=factor(k+1)[,1]~;
%o r[k]=ps[1];
%o for(j=2,#ps,if(ns[primepi(ps[j])]<=ns[primepi(r[k])],r[k]=ps[j]));
%o ns[primepi(r[k])]++);
%o r}
%Y Cf. A197861, A006530.
%K nonn
%O 2,1
%A _Franklin T. AdamsWatters_, Oct 18 2011
