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

2,1

Comments

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

Links

Table of n, a(n) for n=2..76.

Example

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.

Prog

(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}

Crossrefs

Cf. A197861, A006530.

Sequence in context: A276440 A162325 A324371 * A006530 A327398 A323616

Adjacent sequences: A197859 A197860 A197861 * A197863 A197864 A197865

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 18 2011

Status

approved