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A345037 a(n) = Sum_{k=1..n} (-k)^(floor(n/k) - 1).

%I A345037 #16 Jun 12 2021 03:30:17
%S A345037 1,0,3,-1,2,3,6,-12,3,20,23,-49,-46,41,182,-100,-97,-6,-3,-613,418,
%T A345037 1941,1944,-5518,-4765,1364,10205,2629,2632,-1181,-1178,-71404,7463,
%U A345037 105748,127245,-233385,-233382,159813,868586,-335790,-335787,-853276,-853273,-2689757,4163818
%N A345037 a(n) = Sum_{k=1..n} (-k)^(floor(n/k) - 1).
%H A345037 Seiichi Manyama, <a href="/A345037/b345037.txt">Table of n, a(n) for n = 1..5000</a>
%F A345037 G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 + k*x^k).
%F A345037 |a(n)| ~ 3^((n - mod(n,3))/3 - 1). - _Vaclav Kotesovec_, Jun 12 2021
%t A345037 a[n_] := Sum[(-k)^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 45] (* _Amiram Eldar_, Jun 06 2021 *)
%o A345037 (PARI) a(n) = sum(k=1, n, (-k)^(n\k-1));
%o A345037 (PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, x^k*(1-x^k)/(1+k*x^k))/(1-x))
%Y A345037 Cf. A344551, A345036.
%K A345037 sign
%O A345037 1,3
%A A345037 _Seiichi Manyama_, Jun 06 2021