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A072375
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Number of cubefree numbers <= n which are nonsquares having exactly one square in their factorization.
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1
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15
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OFFSET
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1,18
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LINKS
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FORMULA
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a(n) ~ c * n, where c = (6/Pi^2) * Sum_{p prime} 1/(p*(p+1)) = 0.200755... (A271971). - Amiram Eldar, Feb 16 2021
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MATHEMATICA
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cfnsQ[n_]:=Module[{f=FactorInteger[n][[All, 2]]}, Max[f]<3&&Count[f, 2] == 1&&!IntegerQ[Sqrt[n]]]; Accumulate[Table[If[cfnsQ[n], 1, 0], {n, 100}]] (* Harvey P. Dale, May 24 2017 *)
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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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