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A345098 a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).

%I A345098 #22 Aug 27 2022 07:18:56
%S A345098 1,5,29,262,3132,46690,823578,16777484,387420781,10000003165,
%T A345098 285311673777,8916100495209,302875106639207,11112006826381861,
%U A345098 437893890381686113,18446744073726332260,827240261886353544822,39346408075296925042900
%N A345098 a(n) = Sum_{k=1..n} floor(n/k)^floor(n/k).
%H A345098 Seiichi Manyama, <a href="/A345098/b345098.txt">Table of n, a(n) for n = 1..386</a>
%F A345098 G.f.: (1/(1 - x)) * Sum_{j>=1} Sum_{k>=1} (k*x^j)^k * (1 - x^j).
%F A345098 a(n) ~ n^n. - _Vaclav Kotesovec_, Jun 11 2021
%t A345098 a[n_] := Sum[Floor[n/k]^Floor[n/k], {k, 1, n}]; Array[a, 20] (* _Amiram Eldar_, Jun 08 2021 *)
%o A345098 (PARI) a(n) = sum(k=1, n, (n\k)^(n\k));
%o A345098 (PARI) my(N=20, x='x+O('x^N)); Vec(sum(j=1, N, (1-x^j)*sum(k=1, N, (k*x^j)^k))/(1-x))
%Y A345098 Cf. A062796, A345094, A345100.
%K A345098 nonn
%O A345098 1,2
%A A345098 _Seiichi Manyama_, Jun 07 2021