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

1,2

Links

Table of n, a(n) for n=1..58.

Example

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

Mathematica

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

Prog

(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", ")
           )
       )
    )
}

Crossrefs

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

Sequence in context: A095270 A364261 A263827 * A080324 A332951 A165562

Adjacent sequences: A281971 A281972 A281973 * A281975 A281976 A281977

Keyword

nonn

Author

Dimitris Valianatos, Feb 03 2017

Status

approved