A056148 a(0) = 1, a(n) = number of a(k), for 0 <= k <= n-1, that divide n.

1, 1, 2, 2, 4, 2, 5, 2, 7, 2, 8, 2, 9, 2, 10, 3, 11, 2, 12, 2, 14, 4, 12, 2, 18, 3, 12, 5, 16, 2, 18, 2, 18, 5, 14, 6, 26, 2, 15, 4, 23, 2, 22, 2, 22, 9, 18, 2, 29, 3, 22, 5, 22, 2, 29, 7, 27, 5, 21, 2, 37, 2, 21, 11, 26, 7, 31, 2, 25, 6, 33, 2, 41, 2, 25, 13, 27, 7, 32, 2, 36, 9, 26, 2, 45

Offset

0,3

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Example

a(6) = 5 because a(0), a(1), a(2), a(3) and a(5) divide 6.

Maple

a:= proc(n) option remember;
      1+add(`if`(irem(n, a(j))=0, 1, 0), j=1..n-1)
    end:
seq(a(n), n=0..84);  # Alois P. Heinz, Mar 06 2025

Mathematica

a[0] = 1; a[n_] := a[n] = Count[Range[0, n - 1], _?(Divisible[n, a[#]] &)]; Array[a, 100, 0] (* Amiram Eldar, May 26 2024 *)

Prog

(Python)
from sympy import divisors
from collections import Counter
from itertools import count, islice
def agen(): # generator of terms
    an, c = 1, Counter()
    for n in count(1):
        yield an
        c.update([an])
        an = sum(c[d] for d in divisors(n, generator=True) if d in c)
print(list(islice(agen(), 85))) # Michael S. Branicky, Mar 06 2025

Crossrefs

Sequence in context: A140773 A133911 A069932 * A304442 A057567 A353845

Adjacent sequences: A056145 A056146 A056147 * A056149 A056150 A056151

Keyword

easy,nonn,changed

Author

Leroy Quet, Aug 04 2000

Status

approved