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%I #21 May 28 2021 15:52:38
%S 1,3,27,240,3094,45990,821484,16711680,387177517,9990293423,
%T 285263019633,8913939911695,302862111412779,11111328866154037,
%U 437889173336927557,18446462747068745474,827238010832411671962,39346258082152478030126
%N a(n) = Sum_{k=1..n} (-1)^(k+1) * floor(n/k)^n.
%H Seiichi Manyama, <a href="/A344724/b344724.txt">Table of n, a(n) for n = 1..386</a>
%F a(n) = Sum_{k=1,..n} Sum_{d|k} (-1)^(k/d + 1) * (d^n - (d - 1)^n).
%F a(n) = [x^n] (1/(1 - x)) * Sum_{k>=1} (k^n - (k - 1)^n) * x^k/(1 + x^k).
%F a(n) ~ n^n. - _Vaclav Kotesovec_, May 28 2021
%t a[n_] := Sum[(-1)^(k + 1) * Quotient[n, k]^n, {k, 1, n}]; Array[a, 18] (* _Amiram Eldar_, May 27 2021 *)
%o (PARI) a(n) = sum(k=1, n, (-1)^(k+1)*(n\k)^n);
%o (PARI) a(n) = sum(k=1, n, sumdiv(k, d, (-1)^(k/d+1)*(d^n-(d-1)^n)));
%Y Main diagonal of A344726.
%Y Cf. A332469.
%K nonn
%O 1,2
%A _Seiichi Manyama_, May 27 2021
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