cp's OEIS Frontend

A343371 a(n) = 1 + Sum_{d|n, d < n} a(d - 1).

%I A343371 #8 Apr 13 2021 07:13:03
%S A343371 1,1,2,2,3,2,5,2,5,4,6,2,9,2,8,7,7,2,12,2,12,9,9,2,13,5,12,9,12,2,22,
%T A343371 2,14,10,10,10,18,2,15,13,16,2,26,2,20,20,12,2,22,7,23,11,19,2,26,11,
%U A343371 23,16,15,2,30,2,25,26,16,14,36,2,22,13,27,2,32,2,21,28
%N A343371 a(n) = 1 + Sum_{d|n, d < n} a(d - 1).
%H A343371 Seiichi Manyama, <a href="/A343371/b343371.txt">Table of n, a(n) for n = 0..10000</a>
%F A343371 G.f. A(x) satisfies: A(x) = 1 / (1 - x) + x^2 * A(x^2) + x^3 * A(x^3) + x^4 * A(x^4) + ...
%p A343371 a:= proc(n) option remember;
%p A343371       1+add(a(d-1), d=numtheory[divisors](n) minus {n})
%p A343371     end:
%p A343371 seq(a(n), n=0..75);  # _Alois P. Heinz_, Apr 12 2021
%t A343371 a[n_] := a[n] = 1 + Sum[If[d < n, a[d - 1], 0], {d, Divisors[n]}]; Table[a[n], {n, 0, 75}]
%t A343371 nmax = 75; A[_] = 0; Do[A[x_] = 1/(1 - x) + Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) //Normal, nmax + 1]; CoefficientList[A[x], x]
%Y A343371 Cf. A003238, A067824, A068336, A167865.
%K A343371 nonn
%O A343371 0,3
%A A343371 _Ilya Gutkovskiy_, Apr 12 2021