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A345028 a(n) = Sum_{k=1..n} 2^(floor(n/k) - 1).

%I A345028 #18 Jun 07 2021 09:05:12
%S A345028 1,3,6,12,21,41,74,144,275,541,1054,2102,4151,8281,16484,32938,65707,
%T A345028 131391,262464,524878,1049201,2098291,4195444,8390860,16779477,
%U A345028 33558743,67113306,134226304,268444033,536887965,1073758878,2147517156,4295001319,8590001385,17179936018
%N A345028 a(n) = Sum_{k=1..n} 2^(floor(n/k) - 1).
%H A345028 Seiichi Manyama, <a href="/A345028/b345028.txt">Table of n, a(n) for n = 1..3000</a>
%F A345028 G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 - 2*x^k).
%t A345028 a[n_] := Sum[2^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 35] (* _Amiram Eldar_, Jun 06 2021 *)
%o A345028 (PARI) a(n) = sum(k=1, n, 2^(n\k-1));
%o A345028 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1-2*x^k))/(1-x))
%Y A345028 Column k=2 of A345032.
%Y A345028 Cf. A000225, A271860, A345034.
%K A345028 nonn
%O A345028 1,2
%A A345028 _Seiichi Manyama_, Jun 06 2021