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A345100 a(n) = Sum_{k=1..n} k^floor(n/k).

%I A345100 #20 Jun 11 2021 10:45:17
%S A345100 1,3,6,12,17,33,40,68,95,141,152,328,341,461,738,1130,1147,2159,2178,
%T A345100 4068,5841,6997,7020,18198,20723,25001,38798,61546,61575,137445,
%U A345100 137476,223252,342593,408435,485376,1213988,1214025,1476549,2541498,4202810,4202851,8777205
%N A345100 a(n) = Sum_{k=1..n} k^floor(n/k).
%H A345100 Seiichi Manyama, <a href="/A345100/b345100.txt">Table of n, a(n) for n = 1..5000</a>
%F A345100 G.f.: (1/(1 - x)) * Sum_{k>=1} k*x^k * (1 - x^k)/(1 - k*x^k).
%F A345100 a(n) ~ 3^((n - mod(n,3))/3). - _Vaclav Kotesovec_, Jun 11 2021
%t A345100 a[n_] := Sum[k^Floor[n/k], {k, 1, n}]; Array[a, 40] (* _Amiram Eldar_, Jun 08 2021 *)
%o A345100 (PARI) a(n) = sum(k=1, n, k^(n\k));
%o A345100 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k*(1-x^k)/(1-k*x^k))/(1-x))
%Y A345100 Cf. A031971, A055225, A344551, A345098.
%K A345100 nonn
%O A345100 1,2
%A A345100 _Seiichi Manyama_, Jun 08 2021