

A197862


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


1



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
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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(n1), ps);
for(k=1, n1,
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: A273283 A276440 A162325 * A006530 A102095 A109395
Adjacent sequences: A197859 A197860 A197861 * A197863 A197864 A197865


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, Oct 18 2011


STATUS

approved



