A116548 - OEIS

%I #6 Mar 04 2023 18:40:05

%S 1,2,3,2,5,3,7,4,3,5,11,4,13,7,5,8,17,6,19,5,7,11,23,6,5,13,9,7,29,6,

%T 31,8,11,17,7,9,37,19,13,8,41,7,43,11,9,23,47,8,7,10,17,13,53,18,11,

%U 14,19,29,59,10,61,31,21,16,13,11,67,17,23,10,71,12,73,37,15,19,11,13,79,10

%N a(n) = smallest divisor d of n that occurs earlier in the sequence fewer than a(d) times.

%C When n is prime, no smaller divisor is available, so a(n) = n. It can be shown than a(n) < n if n is composite. Similar to Golomb's sequence (A001462), but with the added condition that a(n) divides n.

%H John Tyler Rascoe, <a href="/A116548/b116548.txt">Table of n, a(n) for n = 1..10000</a>

%o (Python)

%o from sympy import divisors

%o def A(maxn):

%o     A = []

%o     for n in range(1,maxn+1):

%o         d = divisors(n)

%o         for j in range(0,len(d)):

%o             if d[j] > len(A): break

%o             if A.count(d[j]) < A[d[j]-1]: break

%o         A.append(d[j])

%o     return(A) # _John Tyler Rascoe_, Mar 04 2023

%Y Cf. A095163, A001462.

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Mar 16 2006