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a(n) = Sum_{k=1..n} k * floor(n/k)^n.
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%I #19 Dec 16 2021 08:41:28

%S 1,6,32,295,3201,48321,828323,16910106,388005909,10019717653,

%T 285409876785,8920506515453,302901435774351,11113364096436947,

%U 437903477186179875,18447307498823123948,827244767844150424228,39346708569526147402819

%N a(n) = Sum_{k=1..n} k * floor(n/k)^n.

%H Seiichi Manyama, <a href="/A350109/b350109.txt">Table of n, a(n) for n = 1..386</a>

%F a(n) = Sum_{k=1..n} k * Sum_{d|k} (d^n - (d - 1)^n)/d.

%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 - x^k)^2.

%F a(n) ~ n^n. - _Vaclav Kotesovec_, Dec 16 2021

%t a[n_] := Sum[k * Floor[n/k]^n, {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, Dec 14 2021 *)

%o (PARI) a(n) = sum(k=1, n, k*(n\k)^n);

%o (PARI) a(n) = sum(k=1, n, k*sumdiv(k, d, (d^n-(d-1)^n)/d));

%Y Main diagonal of A350106.

%Y Cf. A319194, A332469.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Dec 14 2021