A283628 -id:A283628 - cp's OEIS frontend

A068088 n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree.

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

Offset: 1

Amarnath Murthy, Feb 18 2002

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

			36 is a term as 33,34,35 and 37,38,39 are two sets of three consecutive squarefree numbers.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007675, A039833. Equals 4*A283628.

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

<< 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 *)

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

A283668 Numbers n such that 36n - 7, 36n - 6, 36n - 5, 36n - 3, 36n - 2, 36n - 1, 36n + 1, 36n + 2, 36n + 3, 36n + 5, 36n + 6 and 36n + 7 are all squarefree.

Original entry on oeis.org

1, 3, 6, 11, 22, 25, 31, 35, 36, 39, 49, 51, 58, 65, 67, 69, 81, 85, 86, 92, 97, 99, 100, 110, 115, 119, 125, 126, 133, 135, 142, 144, 149, 150, 153, 161, 164, 165, 167, 169, 172, 174, 175, 176, 186, 194, 199, 201, 206, 208, 210, 214, 217, 224, 231, 235, 236, 239, 240, 242, 244, 247, 251

Offset: 1

Juri-Stepan Gerasimov, Mar 13 2017

nonn

			1 is in this sequence because 36*1 - 7 = 29, 36*1 - 6 = 30, 36*1 - 5 = 31, 36*1 - 3 = 33, 36*1 - 2 = 34, 36*1 - 1 = 35, 36*1 + 1 = 37, 36*1 + 2 = 38, 36*1 + 3 = 39, 36*1 + 5 = 41, 36*1 + 6 = 42 and 36*1 + 7 = 43 are all squarefree.

Cf. A005117, A283628.

[n: n in [1..300] | IsSquarefree(36*n-7) and IsSquarefree(36*n-6) and IsSquarefree(36*n-5) and IsSquarefree(36*n-3) and IsSquarefree(36*n-2) and IsSquarefree(36*n-1) and IsSquarefree(36*n+1) and IsSquarefree(36*n+2) and IsSquarefree(36*n+3) and IsSquarefree(36*n+5) and IsSquarefree(36*n+6) and IsSquarefree(36*n+7) ];

Select[Range@ 256, Function[n, Times @@ Boole@ Map[SquareFreeQ, 36 n + Flatten@ {-#, #} &@ Drop[Range@ 7, {4}]] == 1]] (* Michael De Vlieger, Mar 13 2017 *)

isok(n) = forstep(k=36*n - 7, 36*n + 7, [1,1,2,1,1,2,1,1,2,1,1], if(!issquarefree(k), return (0))); 1;
for(n=1, 251, if(isok(n), print1(n,", "))) \\ Indranil Ghosh, Mar 13 2017

a(n) = A283628(9n) = A283628(9n-1) + 1 = A283628(9n+1) - 1.

a(n) ~ k*n where k = Product_{ p prime > 3} p^2/(p^2 - 12) = 3.7192316.... - Michael R Peake, Mar 16 2017

cp's OEIS Frontend

A068088 n-3, n-2, n-1, n+1, n+2 and n+3 are squarefree.

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