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%I #15 Jun 09 2021 10:37:18
%S 1,-1,14,-86,955,-11851,183800,-3273914,67643293,-1571615577,
%T 40838683608,-1170198385960,36717193651461,-1251181160936837,
%U 46033142685018824,-1818354391006060750,76762360864947676457,-3448789505696369210193
%N a(n) = Sum_{k=1..n} (-k)^(n - floor(n/k)).
%H Seiichi Manyama, <a href="/A345107/b345107.txt">Table of n, a(n) for n = 1..387</a>
%F G.f.: Sum_{k>=1} (-k)^(k-1)*x^k * (1 - (-k*x)^k)/((1 - (-k)^(k-1)*x^k) * (1 + k*x)).
%t a[n_] := Sum[(-k)^(n - Floor[n/k]), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2021 *)
%o (PARI) a(n) = sum(k=1, n, (-k)^(n-n\k));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (-k)^(k-1)*x^k*(1-(-k*x)^k)/((1-(-k)^(k-1)*x^k)*(1+k*x))))
%Y Cf. A345037, A345106.
%K sign
%O 1,3
%A _Seiichi Manyama_, Jun 08 2021
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