A281974 Squarefree numbers excluding twin primes.

1, 2, 6, 10, 14, 15, 21, 22, 23, 26, 30, 33, 34, 35, 37, 38, 39, 42, 46, 47, 51, 53, 55, 57, 58, 62, 65, 66, 67, 69, 70, 74, 77, 78, 79, 82, 83, 85, 86, 87, 89, 91, 93, 94, 95, 97, 102, 105, 106, 110, 111, 113, 114, 115, 118, 119, 122, 123

Offset: 1

Author

Dimitris Valianatos, Feb 03 2017

Keywords

• nonn

Examples

			30 is a term because: 30 = 2*3*5 is squarefree and is not a member of a twin primes pair.
		

Crossrefs

Cf. A005117 (squarefree numbers), A001097 (twin primes), A065421 (Brun's constant).

Programs

Mathematica

Select[Range@ 123, SquareFreeQ@ # && ! And[PrimeQ@ #, Total@ Boole@ PrimeQ[# + {-2, 2}] >= 1] &] (* Michael De Vlieger, Feb 04 2017 *)

PARI

{
for(n=1,1000,
     mb=moebius(n);
     if(mb<>0,
         if(isprime(n),
             if(!isprime(n-2)&&!isprime(n+2),
                 print1(n", ")
               ),
              ;print1(n", ")
           )
       )
    )
}