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A173186
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Numbers k such that k^2-1 is not squarefree.
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3
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1, 3, 5, 7, 8, 9, 10, 11, 13, 15, 17, 19, 21, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35, 37, 39, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 53, 55, 57, 59, 61, 62, 63, 64, 65, 67, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 87, 89, 91, 93, 95, 97, 98, 99, 100, 101, 103, 105
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OFFSET
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1,2
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COMMENTS
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The asymptotic density of this sequence is 1 - Product_{p prime} (1 - 2/p^2) = 0.677365... (1 - A065474). - Amiram Eldar, Feb 25 2021
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LINKS
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EXAMPLE
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5 is a term since 5^2-1 = 24 = 2^3*3 is not squarefree.
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MATHEMATICA
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f[n_]:=SquareFreeQ[n]; lst={}; Do[If[f[n^2-1], AppendTo[lst, n]], {n, 6!}]; lst
Select[Range[120], !SquareFreeQ[#^2-1]&] (* Harvey P. Dale, Jul 16 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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