A362232 a(1) = 1; for n > 1, a(n) is number of terms in the first n-1 terms of the sequence that are not proper divisors of a(n-1).

1, 1, 2, 1, 4, 1, 6, 2, 4, 3, 6, 4, 6, 6, 7, 11, 12, 3, 14, 12, 5, 17, 18, 11, 20, 15, 19, 23, 24, 12, 15, 24, 14, 26, 28, 23, 32, 28, 26, 33, 32, 32, 33, 35, 38, 38, 39, 41, 44, 38, 43, 47, 48, 33, 46, 47, 52, 46, 50, 52, 49, 56, 48, 43, 60, 43, 62, 61, 64, 57, 63, 64, 60, 51, 67, 71, 72, 56, 64

Offset: 1

Author

Scott R. Shannon, Apr 12 2023

Keywords

• nonn

Examples

			a(8) = 2 as in the previous 8 - 1 = 7 terms there are two numbers that are not proper divisors of a(7) = 6, namely 4 and 6.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A027751, A032742, A032741, A152271.

Programs

Maple

a:= proc(n) option remember; `if`(n=1, 1, (t-> add(
      `if`(irem(t, a(j))>0 or t=a(j), 1, 0), j=1..n-1))(a(n-1)))
    end:
seq(a(n), n=1..79);  # Alois P. Heinz, May 10 2023

Mathematica

nn = 120; a[1] = 1; Do[Set[{c, m}, {0, a[n - 1]}]; Do[If[And[# < m, Divisible[m, #]] &[a[i]], c++], {i, n}]; a[n] = n - c - 1, {n, 2, nn}]; Array[a, nn] (* Michael De Vlieger, May 10 2023 *)