cp's OEIS Frontend

A344551 a(n) = Sum_{k=1..n} k^floor((n-k)/k).

%I A344551 #13 Jun 06 2021 09:00:15
%S A344551 1,2,3,5,6,11,12,20,27,40,41,93,94,133,208,328,329,658,659,1217,1746,
%T A344551 2269,2270,5768,6269,8330,12777,20253,20254,45253,45254,74390,113867,
%U A344551 146652,161211,401275,401276,532367,886818,1412574,1412575,3053234,3053235,4889475,8396664
%N A344551 a(n) = Sum_{k=1..n} k^floor((n-k)/k).
%H A344551 Seiichi Manyama, <a href="/A344551/b344551.txt">Table of n, a(n) for n = 1..5000</a>
%F A344551 a(n) ~ 3^((n - 3 - mod(n,3))/3). - _Vaclav Kotesovec_, May 28 2021
%F A344551 G.f.: (1/(1 - x)) * Sum_{k>=1} x^k * (1 - x^k)/(1 - k*x^k). - _Seiichi Manyama_, Jun 06 2021
%t A344551 Table[Sum[k^Floor[(n - k)/k], {k, n}], {n, 80}]
%o A344551 (PARI) a(n) = sum(k=1, n, k^(n\k-1)); \\ _Seiichi Manyama_, Jun 06 2021
%o A344551 (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)) \\ _Seiichi Manyama_, Jun 06 2021
%Y A344551 Cf. A002541, A006218, A153485.
%K A344551 nonn
%O A344551 1,2
%A A344551 _Wesley Ivan Hurt_, May 22 2021