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A345108 a(n) = Sum_{k=1..n} 2^(n - floor(n/k)).

%I A345108 #15 Jun 09 2021 10:37:25
%S A345108 1,3,9,21,57,121,305,657,1505,3233,7489,15169,34433,72833,156929,
%T A345108 325889,717313,1462785,3187713,6538241,13846529,28739585,61673473,
%U A345108 124063745,263856129,544481281,1139032065,2326282241,4920999937,9924804609,20923351041,42635165697
%N A345108 a(n) = Sum_{k=1..n} 2^(n - floor(n/k)).
%H A345108 Seiichi Manyama, <a href="/A345108/b345108.txt">Table of n, a(n) for n = 1..3000</a>
%F A345108 G.f.: (1/(1 - 2*x)) * Sum_{k>=1} 2^(k-1)*x^k * (1 - (2*x)^k)/(1 - 2^(k-1)*x^k).
%t A345108 a[n_] := Sum[2^(n - Floor[n/k]), {k, 1, n}]; Array[a, 30] (* _Amiram Eldar_, Jun 08 2021 *)
%o A345108 (PARI) a(n) = sum(k=1, n, 2^(n-n\k));
%o A345108 (PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, 2^(k-1)*x^k*(1-(2*x)^k)/(1-2^(k-1)*x^k))/(1-2*x))
%Y A345108 Cf. A345028, A345109.
%K A345108 nonn
%O A345108 1,2
%A A345108 _Seiichi Manyama_, Jun 08 2021