A384336 a(1) = 1, a(2) = 2. For n > 2, a(n) = number of a(k), k = 1..n-2 such that a(k) divides a(n-1).

1, 2, 1, 1, 2, 4, 5, 3, 3, 4, 6, 7, 3, 5, 4, 7, 4, 8, 9, 6, 9, 7, 5, 5, 6, 10, 9, 8, 10, 10, 11, 3, 6, 12, 17, 3, 7, 6, 14, 9, 11, 4, 9, 12, 21, 12, 22, 7, 7, 8, 12, 23, 3, 8, 13, 3, 9, 15, 14, 12, 26, 6, 17, 4, 10, 12, 29, 3, 10, 13, 4, 11, 5, 7, 9, 17, 5, 8

Offset

1,2

Comments

1 appears 3 times and 2 appears 2 times, all other numbers are conjectured to appear infinitely many times. The first occurrence of an odd prime is followed by 3, see Example, and the order of first appearances of primes starts: 2,5,3,7,11,19,23,13.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..16384

Example

Since a(1) = 1, and a(2) = 2, a(3) must be 1 since there is only one term (a(1) = 1) which is a divisor of 2. Then a(4) = 1 because a(1) = 1 is the only prior divisor of a(3) = 1.

Maple

a:= proc(n) option remember; `if`(n<3, n, add(
     `if`(irem(a(n-1), a(j))=0, 1, 0), j=1..n-2))
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 01 2025

Mathematica

nn = 120; Array[Set[a[#], #] &, 2]; j = 2; Do[k = Count[Array[a, n - 2], _?(Divisible[j, #] &)]; Set[{a[n], j}, {k, k}], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Jun 01 2025 *)

Crossrefs

Cf. A000005.

Sequence in context: A333272 A352501 A119558 * A333450 A210112 A024735

Adjacent sequences: A384333 A384334 A384335 * A384337 A384338 A384339

Keyword

nonn

Author

David James Sycamore, May 28 2025

Extensions

More terms from Alois P. Heinz, Jun 01 2025

Status

approved