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A068088
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n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree.
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5
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4, 32, 36, 40, 68, 104, 108, 112, 140, 180, 184, 212, 216, 220, 256, 284, 320, 356, 392, 396, 400, 432, 436, 464, 468, 500, 544, 612, 616, 644, 680, 716, 756, 760, 788, 792, 796, 860, 896, 900, 904, 936, 940, 968, 1004, 1008, 1040, 1044, 1112, 1116, 1120, 1156, 1188, 1192, 1220, 1256, 1260, 1264
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OFFSET
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1,1
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COMMENTS
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No four consecutive numbers can all be squarefree, as one of them is divisible by 2^2 = 4.
From 28 to 44 there are 12 squarefree numbers among 15 consecutive integers. Other examples are 100 to 116 and 212 to 228.
The largest possible run of consecutive multiples of 4 in the sequence is 3: If n, n+4 and n+8 are in the sequence then n+4 and hence n-5 and n+13 must be divisible by 9, so neither n-4 nor n+12 can be in the sequence. - Ulrich Schimke, Apr 13 2002
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LINKS
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EXAMPLE
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36 is a term as 33,34,35 and 37,38,39 are two sets of three consecutive squarefree numbers.
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MAPLE
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select(t -> andmap(numtheory:-issqrfree, [t-3, t-2, t-1, t+1, t+2, t+3]), [seq(i, i=4..2000, 4)]); # Robert Israel, Jun 05 2018
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MATHEMATICA
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<< NumberTheory`NumberTheoryFunctions` lst={}; Do[If[SquareFreeQ[n-1]&&SquareFreeQ[n+1]&&SquareFreeQ[n-2]&&SquareFreeQ[n+2]&&SquareFreeQ[n-3]&&SquareFreeQ[n+3], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 26 2009 *)
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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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Corrected and extended by Ulrich Schimke, Apr 13 2002
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STATUS
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approved
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