%I #5 Feb 19 2022 07:23:08
%S 1,1,1,2,2,4,4,8,9,13,13,25,25,33,37,57,57,83,83,117,125,151,151,233,
%T 237,287,305,387,387,503,503,649,675,789,805,1073,1073,1239,1289,1607,
%U 1607,1955,1955,2309,2419,2721,2721,3465,3481,4007,4121,4795,4795,5643,5695
%N a(1) = 1; a(n) = a(n-1) + Sum_{d|n, 1 < d < n} a(n/d) * a(d).
%F G.f.: ( x + Sum_{i>=2} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).
%t a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[If[1 < d < n, a[n/d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 55}]
%Y Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787.
%K nonn
%O 1,4
%A _Ilya Gutkovskiy_, Feb 19 2022