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A345094 a(n) = Sum_{k=1..n} floor(n/k)^(floor(n/k) - 1).

%I A345094 #20 Aug 27 2022 07:18:51
%S A345094 1,3,11,68,630,7790,117664,2097224,43046801,1000000643,25937425245,
%T A345094 743008378547,23298085130341,793714773371879,29192926025508929,
%U A345094 1152921504608944840,48661191875668966346,2185911559738739586562,104127350297911284587436
%N A345094 a(n) = Sum_{k=1..n} floor(n/k)^(floor(n/k) - 1).
%H A345094 Seiichi Manyama, <a href="/A345094/b345094.txt">Table of n, a(n) for n = 1..387</a>
%F A345094 G.f.: (1/(1 - x)) * Sum_{j>=1} Sum_{k>=1} k^(k-1) * x^(j*k) * (1 - x^j).
%t A345094 a[n_] := Sum[Floor[n/k]^(Floor[n/k] - 1), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2021 *)
%o A345094 (PARI) a(n) = sum(k=1, n, (n\k)^(n\k-1));
%o A345094 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^j)*sum(k=1, N, k^(k-1)*x^(j*k)))/(1-x))
%Y A345094 Cf. A060946, A262843, A344551, A345030, A345098.
%K A345094 nonn
%O A345094 1,2
%A A345094 _Seiichi Manyama_, Jun 07 2021