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%I #8 Feb 20 2022 11:12:06
%S 1,2,4,8,13,22,32,48,67,93,120,164,209,266,331,418,506,626,747,905,
%T 1076,1276,1477,1755,2039,2370,2723,3149,3576,4112,4649,5295,5971,
%U 6737,7519,8501,9484,10590,11744,13109,14475,16092,17710,19561,21504,23650,25797,28386,30986,33903
%N a(1) = 1; a(n) = a(n-1) + Sum_{k=2..n} a(floor(n/k)).
%C Partial sums of A320225.
%F G.f. A(x) satisfies: A(x) = x/(1 - x) + (1/(1 - x)^2) * Sum_{k>=2} (1 - x^k) * A(x^k).
%t a[1] = 1; a[n_] := a[n] = a[n - 1] + Sum[a[Floor[n/k]], {k, 2, n}]; Table[a[n], {n, 1, 50}]
%Y Cf. A001519, A022825, A025523, A033485, A078346, A320225, A351621.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 20 2022