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

1,2

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

Prog

(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

Crossrefs

Cf. A095163, A001462.

Sequence in context: A072505 A095163 A033677 * A348582 A346701 A347044

Adjacent sequences: A116545 A116546 A116547 * A116549 A116550 A116551

Keyword

nonn

Author

Franklin T. Adams-Watters, Mar 16 2006

Status

approved