A109289 Composite numbers which are not of the form p*q + 1, where p and q are distinct primes.

4, 6, 8, 9, 10, 12, 14, 18, 20, 21, 24, 25, 26, 28, 30, 32, 33, 38, 42, 44, 45, 46, 48, 49, 50, 51, 54, 55, 57, 60, 62, 64, 65, 68, 69, 72, 74, 76, 77, 80, 81, 82, 84, 85, 90, 91, 93, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 114, 115, 117, 118, 121, 122, 125, 126, 128

Offset: 1

Author

Giovanni Teofilatto, Aug 20 2005

Keywords

• easy
• nonn

Crossrefs

Cf. A109287, A109288, A109290.

Programs

Mathematica

Select[Range[2, 130], ! (PrimeQ[ # ] || (Plus @@ Last /@ FactorInteger[ # - 1] == 2 && Length[FactorInteger[ # - 1]] == 2)) &] (* Ray Chandler, Aug 25 2005 *)
fQ[n_] := Last /@ FactorInteger[n] != {1, 1}; Select[ Range[2, 128], !PrimeQ[ # ] && fQ[ # - 1] &] (* Robert G. Wilson v *)

Extensions

Extended by Robert G. Wilson v and Ray Chandler, Aug 25 2005