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A087049
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Characteristic sequence for numbers n>=0 that are either squares or have a square > 1 as factor.
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4
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1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1
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OFFSET
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0,1
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COMMENTS
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a(0)=1, a(1)=1, n>=2: a(n)=1 if isquarefree(n)=false else 0.
Except for a(0)=1 and a(1)=1 this is the bit-flipped unsigned Moebius sequence abs(A008683(n)), n>=2.
For n>=2: a(n)=1 iff n is from A013929 (not squarefree).
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LINKS
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FORMULA
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a(n) = 1 if n is a perfect square (A000290) or has some square > 1 as a factor, else 0.
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=0..m} a(k) = 1 - 6/Pi^2 (A229099). - Amiram Eldar, Jan 19 2024
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EXAMPLE
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a(4) = 1 because 4 is a square; a(8) = 1 because 8 = 2^2 * 2.
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MAPLE
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1, 1, seq(`if`(numtheory:-issqrfree(n), 0, 1), n=2..100); # Robert Israel, Nov 17 2017
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MATHEMATICA
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Array[If[# <= 1, 1, 1 - Abs@ MoebiusMu@ #] &, 105, 0] (* Michael De Vlieger, Nov 17 2017 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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