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%I #7 Feb 20 2022 11:12:15
%S 1,3,6,12,19,32,46,69,96,133,171,234,298,379,471,595,720,891,1063,
%T 1288,1531,1815,2100,2496,2900,3371,3873,4479,5086,5848,6611,7530,
%U 8491,9580,10691,12088,13486,15059,16700,18642,20585,22885,25186,27818,30580,33630,36681,40363,44060,48208
%N a(1) = 1; a(n) = 1 + a(n-1) + Sum_{k=2..n} a(floor(n/k)).
%C Partial sums of A345139.
%F G.f. A(x) satisfies: A(x) = ( x + Sum_{k>=2} (1 - x^k) * A(x^k) ) / (1 - x)^2.
%t a[1] = 1; a[n_] := a[n] = 1 + a[n - 1] + Sum[a[Floor[n/k]], {k, 2, n}]; Table[a[n], {n, 1, 50}]
%Y Cf. A001906, A022825, A025523, A078346, A102378, A345139, A351620.
%K nonn
%O 1,2
%A _Ilya Gutkovskiy_, Feb 20 2022