A332468 - OEIS

%I #30 Nov 02 2023 17:52:39

%S 1,3,25,239,3091,45863,821227,16711423,387138661,9990174303,

%T 285262663291,8913906888703,302861978789371,11111328334033327,

%U 437889112287422401,18446462446101903615,827238009323454485641,39346257879101283645743,1978418304199236175597105

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

%H Seiichi Manyama, <a href="/A332468/b332468.txt">Table of n, a(n) for n = 1..386</a>

%F a(n) ~ n^n. - _Vaclav Kotesovec_, May 28 2021

%t Table[Sum[MoebiusMu[k] Floor[n/k]^n, {k, 1, n}], {n, 1, 19}]

%t 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 (PARI) a(n)={sum(k=1, n, moebius(k) * floor(n/k)^n)} \\ _Andrew Howroyd_, Feb 13 2020

%o (Magma) [&+[MoebiusMu(k)*Floor(n/k)^n:k in [1..n]]:n in [1..20]]; // _Marius A. Burtea_, Feb 13 2020

%o (Python)

%o from functools import lru_cache

%o @lru_cache(maxsize=None)

%o def A344527_T(n,k):

%o     if n == 0:

%o         return 0

%o     c, j, k1 = 1, 2, n//2

%o     while k1 > 1:

%o         j2 = n//k1 + 1

%o         c += (j2-j)*A344527_T(k1,k)

%o         j, k1 = j2, n//j2

%o     return n*(n**(k-1)-1)-c+j

%o def A332468(n): return A344527_T(n,n) # _Chai Wah Wu_, Nov 02 2023

%Y Main diagonal of A344527.

%Y Cf. A008683, A018805, A071778, A082540, A082544, A332469, A343978.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Feb 13 2020