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 A068088 n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree. 5
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 EXAMPLE 36 is a term as 33,34,35 and 37,38,39 are two sets of three consecutive squarefree numbers. MAPLE 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 MATHEMATICA << 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 *) CROSSREFS Cf. A007675, A039833. Equals 4*A283628. Sequence in context: A196247 A196250 A290809 * A118901 A275713 A114076 Adjacent sequences:  A068085 A068086 A068087 * A068089 A068090 A068091 KEYWORD easy,nonn AUTHOR Amarnath Murthy, Feb 18 2002 EXTENSIONS Corrected and extended by Ulrich Schimke, Apr 13 2002 Further correction from Harvey P. Dale, May 01 2002 Offset changed to 1 by Michel Marcus, May 24 2014 STATUS approved

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Last modified September 22 16:59 EDT 2019. Contains 327311 sequences. (Running on oeis4.)