_Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), _, Oct 18 2011

proposed

approved

editing

proposed

allocated for Franklin T. Adams-Watters

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

2,1

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

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.

(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}

Cf. A197861, A006530.

allocated

nonn

Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 18 2011

approved

editing

allocated for Franklin T. Adams-Watters

allocated

approved