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A197862 Prime divisor of n which appears the fewest times previously in the sequence, with ties to the larger prime. 1

%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(n-1),ps);

%o for(k=1,n-1,

%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. Adams-Watters_, Oct 18 2011

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Last modified October 16 08:03 EDT 2018. Contains 316259 sequences. (Running on oeis4.)