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Numbers n such that n-1, n and n+1 are all squarefree semiprimes.
9

%I #39 Jul 17 2021 16:46:28

%S 34,86,94,142,202,214,218,302,394,446,634,698,922,1042,1138,1262,1346,

%T 1402,1642,1762,1838,1894,1942,1982,2102,2182,2218,2306,2362,2434,

%U 2462,2518,2642,2722,2734,3098,3386,3602,3694,3866,3902,3958,4286,4414

%N Numbers n such that n-1, n and n+1 are all squarefree semiprimes.

%C A subsequence of A169834. - _M. F. Hasler_, Oct 26 2014

%H Giovanni Resta, <a href="/A248201/b248201.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Semiprime">Semiprime</a>

%F a(n) = A039833(n) + 1. - _Michel Marcus_, Oct 25 2014

%F a(n) = 2 * A195685(n). - _Torlach Rush_, Jun 25 2021

%e 33, 34 and 35 factor as 3*11, 2*17 and 5*7, respectively. No smaller such trio exists, so a(1)=34.

%t lst={}; Do[z=n^3 + 3 n^2 + 2 n; If[PrimeOmega[z/n]==PrimeOmega[z/(n + 2)]==4 && PrimeNu[z]==6, AppendTo[lst, n + 1]], {n, 1, 6000, 2}]; lst (* _Vincenzo Librandi_, Jul 24 2015 *)

%t SequencePosition[Table[If[SquareFreeQ[n]&&PrimeOmega[n]==2,1,0],{n,4500}],{1,1,1}][[All,1]]+1 (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 11 2018 *)

%o (PARI) sq(n)=bigomega(n)==2 && omega(n)==2;

%o for(n=3,10^4,if(sq(n-1)&&sq(n)&&sq(n+1),print1(n,", ")));

%o \\ _Joerg Arndt_, Oct 18 2014

%Y Cf. A006881, A039833, A169834, A195685, A248202, A248203, A248204, A259349, A259350, A259801.

%K nonn

%O 1,1

%A _James G. Merickel_, Oct 03 2014