A116548 a(n) = smallest divisor d of n that occurs earlier in the sequence fewer than a(d) times.

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, 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, 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

Offset: 1

Author

Franklin T. Adams-Watters, Mar 16 2006

Keywords

• nonn

Comments

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.

Links

• John Tyler Rascoe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A095163, A001462.

Programs

Python

from sympy import divisors
def A(maxn):
    A = []
    for n in range(1,maxn+1):
        d = divisors(n)
        for j in range(0,len(d)):
            if d[j] > len(A): break
            if A.count(d[j]) < A[d[j]-1]: break
        A.append(d[j])
    return(A) # John Tyler Rascoe, Mar 04 2023