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A345106 a(n) = Sum_{k=1..n} k^(n - floor(n/k)).

%I A345106 #17 Jun 09 2021 10:37:15
%S A345106 1,3,14,96,971,12015,184286,3283598,67676125,1572527901,40843114146,
%T A345106 1170338862814,36718016941445,1251213685475261,46033362584427670,
%U A345106 1818364700307111794,76762441669319061911,3448793841153099408185,164309637864524321789042
%N A345106 a(n) = Sum_{k=1..n} k^(n - floor(n/k)).
%H A345106 Seiichi Manyama, <a href="/A345106/b345106.txt">Table of n, a(n) for n = 1..387</a>
%F A345106 G.f.: Sum_{k>=1} k^(k-1)*x^k * (1 - (k*x)^k)/((1 - k^(k-1)*x^k) * (1 - k*x)).
%t A345106 a[n_] := Sum[k^(n - Floor[n/k]), {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2021 *)
%o A345106 (PARI) a(n) = sum(k=1, n, k^(n-n\k));
%o A345106 (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 A345106 Cf. A076015, A344551, A345107.
%K A345106 nonn
%O A345106 1,2
%A A345106 _Seiichi Manyama_, Jun 08 2021