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A332468 a(n) = Sum_{k=1..n} mu(k) * floor(n/k)^n.

%I A332468 #30 Nov 02 2023 17:52:39
%S A332468 1,3,25,239,3091,45863,821227,16711423,387138661,9990174303,
%T A332468 285262663291,8913906888703,302861978789371,11111328334033327,
%U A332468 437889112287422401,18446462446101903615,827238009323454485641,39346257879101283645743,1978418304199236175597105
%N A332468 a(n) = Sum_{k=1..n} mu(k) * floor(n/k)^n.
%H A332468 Seiichi Manyama, <a href="/A332468/b332468.txt">Table of n, a(n) for n = 1..386</a>
%F A332468 a(n) ~ n^n. - _Vaclav Kotesovec_, May 28 2021
%t A332468 Table[Sum[MoebiusMu[k] Floor[n/k]^n, {k, 1, n}], {n, 1, 19}]
%t A332468 b[n_, k_] := b[n, k] = n^k - Sum[b[Floor[n/j], k], {j, 2, n}]; a[n_] := b[n, n]; Table[a[n], {n, 1, 19}]
%o A332468 (PARI) a(n)={sum(k=1, n, moebius(k) * floor(n/k)^n)} \\ _Andrew Howroyd_, Feb 13 2020
%o A332468 (Magma) [&+[MoebiusMu(k)*Floor(n/k)^n:k in [1..n]]:n in [1..20]]; // _Marius A. Burtea_, Feb 13 2020
%o A332468 (Python)
%o A332468 from functools import lru_cache
%o A332468 @lru_cache(maxsize=None)
%o A332468 def A344527_T(n,k):
%o A332468     if n == 0:
%o A332468         return 0
%o A332468     c, j, k1 = 1, 2, n//2
%o A332468     while k1 > 1:
%o A332468         j2 = n//k1 + 1
%o A332468         c += (j2-j)*A344527_T(k1,k)
%o A332468         j, k1 = j2, n//j2
%o A332468     return n*(n**(k-1)-1)-c+j
%o A332468 def A332468(n): return A344527_T(n,n) # _Chai Wah Wu_, Nov 02 2023
%Y A332468 Main diagonal of A344527.
%Y A332468 Cf. A008683, A018805, A071778, A082540, A082544, A332469, A343978.
%K A332468 nonn
%O A332468 1,2
%A A332468 _Ilya Gutkovskiy_, Feb 13 2020