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A283628 Numbers n such that 4n - 3, 4n - 2, 4n - 1, 4n + 1, 4n + 2 and 4n + 3 are all squarefree.

%I A283628 #32 Sep 08 2022 08:46:18
%S A283628 1,8,9,10,17,26,27,28,35,45,46,53,54,55,64,71,80,89,98,99,100,108,109,
%T A283628 116,117,125,136,153,154,161,170,179,189,190,197,198,199,215,224,225,
%U A283628 226,234,235,242,251,252,260,261,278,279,280,289,297,298,305,314,315,316,323,324,325,334,341,350
%N A283628 Numbers n such that 4n - 3, 4n - 2, 4n - 1, 4n + 1, 4n + 2 and 4n + 3 are all squarefree.
%H A283628 Charles R Greathouse IV, <a href="/A283628/b283628.txt">Table of n, a(n) for n = 1..10000</a>
%F A283628 a(n) ~ kn with k around 5.42. - _Charles R Greathouse IV_, Mar 13 2017
%F A283628 a(n) ~ kn where k = Product_{p prime > 2} p^2/(p^2-6). - _Michael R Peake_, Mar 17 2017
%e A283628 1 is in this sequence because 4*1 - 3 = 1, 4*1 - 2 = 2, 4*1 - 1 = 3, 4*1 + 1 = 5, 4*1 + 2 = 6 and 4*1 + 3 = 7 are all squarefree.
%t A283628 Select[Range@ 350, Function[n, Times @@ Boole@ Map[SquareFreeQ, 4 n + Flatten@ {-#, #} &@ Range@ 3] == 1]] (* _Michael De Vlieger_, Mar 17 2017 *)
%t A283628 Select[Range[400],AllTrue[4#+{1,2,3,-1,-2,-3},SquareFreeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Nov 30 2019 *)
%o A283628 (Magma) [n: n in [1..300] | IsSquarefree(4*n-3) and IsSquarefree(4*n-2) and IsSquarefree(4*n-1) and IsSquarefree(4*n+1) and IsSquarefree(4*n+2) and IsSquarefree(4*n+3) ];
%o A283628 (PARI) is(n)=forstep(k=4*n-3,4*n+3,[1,1,2,1,1], if(!issquarefree(k), return(0))); 1 \\ _Charles R Greathouse IV_, Mar 13 2017
%Y A283628 Cf. A005117.
%K A283628 nonn
%O A283628 1,2
%A A283628 _Juri-Stepan Gerasimov_, Mar 13 2017