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%I #23 Oct 04 2023 03:54:49
%S 1,8,40,345,3303,50225,833569,17045934,388654659,10039636255,
%T 285508661853,8924967326015,302927979357701,11114722212099135,
%U 437913155876193839,18447871416712820782,827249276230172525622,39347009369000530723017
%N a(n) = Sum_{k=1..n} k^2 * floor(n/k)^n.
%H Seiichi Manyama, <a href="/A350125/b350125.txt">Table of n, a(n) for n = 1..386</a>
%F a(n) = Sum_{k=1..n} k^2 * Sum_{d|k} (d^n - (d - 1)^n)/d^2.
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k * (1 + x^k)/(1 - x^k)^3.
%F a(n) ~ n^n. - _Vaclav Kotesovec_, Dec 16 2021
%t a[n_] := Sum[k^2 * Floor[n/k]^n, {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Oct 04 2023 *)
%o (PARI) a(n) = sum(k=1, n, k^2*(n\k)^n);
%o (PARI) a(n) = sum(k=1, n, k^2*sumdiv(k, d, (d^n-(d-1)^n)/d^2));
%Y Cf. A332469, A350109, A350123, A350124, A350128.
%K nonn
%O 1,2
%A _Seiichi Manyama_, Dec 15 2021
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