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1, -1, -2, -1, -2, 0, -1, -1, -1, 1, 0, -1, -2, 0, 1, 1, 0, 0, -1, -2, -1, 1, 0, 0, 0, 2, 2, 1, 0, -2, -3, -3, -2, 0, 1, 1, 0, 2, 3, 3, 2, 0, -1, -2, -2, 0, -1, -1, -1, -1, 0, -1, -2, -2, -1, -1, 0, 2, 1, 2, 1, 3, 3, 3, 4, 2, 1, 0, 1, -1, -2, -2, -3, -1, -1, -2, -1, -3, -4, -4, -4, -2, -3, -2, -1, 1, 2, 2, 1, 1, 2, 1, 2, 4, 5, 5, 4, 4, 4, 4, 3, 1, 0, 0, -1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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FORMULA
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G.f. Sum_{n >= 1} a(n)*(x^n)/((1-x^n)*(x^(n+1)-1))*x = -(x^2) and -1/x. [Mats Granvik, Oct 11 2010]
a(1)=1, then for n>=2, Sum_{k=1..n} a(floor(n/k)) = 0. - Benoit Cloitre, Feb 21 2013
G.f. A(x) satisfies x * (1 - x) = Sum_{k>=1} (1 - x^k) * A(x^k). - Seiichi Manyama, Mar 31 2023
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MATHEMATICA
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Accumulate@ Array[MoebiusMu[#] - If[OddQ@ #, 0, MoebiusMu[#/2]] &, 106] (* Michael De Vlieger, Mar 31 2021 *)
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PROG
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(PARI) a(n)=my(s); forstep(k=bitor(n\4+1, 1), n\2, 2, s-=moebius(k)); forstep(k=bitor(n\2+1, 1), n, 2, s+=moebius(k)); s \\ Charles R Greathouse IV, Feb 07 2013
(Python)
from functools import lru_cache
@lru_cache(maxsize=None)
if n == 1:
return 1
c, j = n+1, 2
k1 = n//j
while k1 > 1:
j2 = n//k1 + 1
j, k1 = j2, n//j2
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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