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%I A068088 #19 Jun 06 2018 09:08:37
%S A068088 4,32,36,40,68,104,108,112,140,180,184,212,216,220,256,284,320,356,
%T A068088 392,396,400,432,436,464,468,500,544,612,616,644,680,716,756,760,788,
%U A068088 792,796,860,896,900,904,936,940,968,1004,1008,1040,1044,1112,1116,1120,1156,1188,1192,1220,1256,1260,1264
%N A068088 n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree.
%C A068088 No four consecutive numbers can all be squarefree, as one of them is divisible by 2^2 = 4.
%C A068088 From 28 to 44 there are 12 squarefree numbers among 15 consecutive integers. Other examples are 100 to 116 and 212 to 228.
%C A068088 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
%H A068088 Robert Israel, <a href="/A068088/b068088.txt">Table of n, a(n) for n = 1..10000</a>
%e A068088 36 is a term as 33,34,35 and 37,38,39 are two sets of three consecutive squarefree numbers.
%p A068088 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
%t A068088 << 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 *)
%Y A068088 Cf. A007675, A039833. Equals 4*A283628.
%K A068088 easy,nonn
%O A068088 1,1
%A A068088 _Amarnath Murthy_, Feb 18 2002
%E A068088 Corrected and extended by Ulrich Schimke, Apr 13 2002
%E A068088 Further correction from _Harvey P. Dale_, May 01 2002
%E A068088 Offset changed to 1 by _Michel Marcus_, May 24 2014

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