%I #18 May 10 2023 22:40:48
%S 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,
%T 24,12,15,24,14,26,28,23,32,28,26,33,32,32,33,35,38,38,39,41,44,38,43,
%U 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
%N 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).
%H Scott R. Shannon, <a href="/A362232/b362232.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%p a:= proc(n) option remember; `if`(n=1, 1, (t-> add(
%p `if`(irem(t, a(j))>0 or t=a(j), 1, 0), j=1..n-1))(a(n-1)))
%p end:
%p seq(a(n), n=1..79); # _Alois P. Heinz_, May 10 2023
%t 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 *)
%Y Cf. A027751, A032742, A032741, A152271.
%K nonn
%O 1,3
%A _Scott R. Shannon_, Apr 12 2023