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A332468
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a(n) = Sum_{k=1..n} mu(k) * floor(n/k)^n.
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4
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1, 3, 25, 239, 3091, 45863, 821227, 16711423, 387138661, 9990174303, 285262663291, 8913906888703, 302861978789371, 11111328334033327, 437889112287422401, 18446462446101903615, 827238009323454485641, 39346257879101283645743, 1978418304199236175597105
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OFFSET
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1,2
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LINKS
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FORMULA
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MATHEMATICA
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Table[Sum[MoebiusMu[k] Floor[n/k]^n, {k, 1, n}], {n, 1, 19}]
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}]
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PROG
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(PARI) a(n)={sum(k=1, n, moebius(k) * floor(n/k)^n)} \\ Andrew Howroyd, Feb 13 2020
(Magma) [&+[MoebiusMu(k)*Floor(n/k)^n:k in [1..n]]:n in [1..20]]; // Marius A. Burtea, Feb 13 2020
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 0:
return 0
c, j, k1 = 1, 2, n//2
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
return n*(n**(k-1)-1)-c+j
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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