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A073312
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Number of nonsquarefree numbers in the reduced residue system of n.
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3
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0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 3, 0, 4, 1, 2, 1, 5, 0, 6, 1, 4, 1, 7, 0, 7, 2, 5, 3, 11, 0, 11, 3, 7, 3, 9, 1, 13, 3, 7, 2, 14, 1, 14, 3, 6, 4, 16, 1, 16, 3, 11, 5, 20, 2, 15, 4, 13, 5, 22, 1, 23, 5, 10, 6, 18, 2, 25, 6, 15, 2, 26, 2, 27, 6, 11, 7, 24, 2, 29, 4, 17, 8, 31, 1, 23, 8, 17, 8, 33, 1, 28
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OFFSET
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1,9
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^2, where c = (3/Pi^2) * (1 - A065463) = 0.0898387... . - Amiram Eldar, Dec 07 2023
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EXAMPLE
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n=15, there are A000010(15)=8 residues: 1, 2, 4=2^2, 7, 8=2^3, 11, 13 and 14; two of them are not squarefree: 4 and 8, therefore a(15)=2.
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MATHEMATICA
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a[n_] := EulerPhi[n] - Module[{rad = Times @@ (First@# & /@ FactorInteger[n])}, Sum[MoebiusMu[k*rad]^2, {k, 1, n}]]; Array[a, 100] (* Amiram Eldar, Mar 08 2020 *)
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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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