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A072284
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Numbers k begins a new chain of squarefree integers. I.e., k is squarefree but k-1 is not.
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5
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1, 5, 10, 13, 17, 19, 21, 26, 29, 33, 37, 41, 46, 51, 53, 55, 57, 61, 65, 69, 73, 77, 82, 85, 89, 91, 93, 97, 101, 105, 109, 113, 118, 122, 127, 129, 133, 137, 141, 145, 149, 151, 154, 157, 161, 163, 165, 170, 173, 177, 181, 185, 190, 193, 197, 199, 201, 205, 209
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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/zeta(2) - Product_{p prime} (1 - 2/p^2) = A059956 - A065474 = 0.2852930029... (Matomäki et al., 2016) - Amiram Eldar, Feb 14 2021
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LINKS
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Eric Weisstein's World of Mathematics, Squarefree.
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FORMULA
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EXAMPLE
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1 begins a new chain 1, 2, 3 of squarefree integers. 4 is not squarefree. Then 5 begins a new chain 5, 6, 7 of squarefree integers. Hence 1 and 5 are terms of the sequence.
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MATHEMATICA
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Select[Range[100], MoebiusMu[# - 1] == 0 && Abs[MoebiusMu[#]] == 1 &] (* Amiram Eldar, Feb 14 2021 *)
SequencePosition[Table[If[SquareFreeQ[n], 1, 0], {n, 0, 250}], {0, 1}][[All, 2]]-1 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 24 2021 *)
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PROG
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(PARI) n=1; for(k=1, 100, while(!issquarefree(n), n=n+1); print1(n", "); while(issquarefree(n), n=n+1))
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CROSSREFS
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KEYWORD
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easy,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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