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

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, 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, 29, 59, 5, 61, 31, 7, 2, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19

Offset: 2

Author

Franklin T. Adams-Watters, Oct 18 2011

Keywords

• nonn

Comments

Up to n = 100, this differs from the greatest prime factor function A006530 only at n = 24, 48, 50, 80, and 98.

Examples

			The only prime divisor of 4 is 2, so a(4) = 2.
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.
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.
		

Crossrefs

Cf. A197861, A006530.

Programs

PARI

al(n)={local(ns=vector(primepi(n)),r=vector(n-1),ps);
  for(k=1,n-1,
    ps=factor(k+1)[,1]~;
    r[k]=ps[1];
    for(j=2,#ps,if(ns[primepi(ps[j])]<=ns[primepi(r[k])],r[k]=ps[j]));
    ns[primepi(r[k])]++);
  r}