A109290 Composite numbers which are not of the forms p*q -+ 1, where p and q are (not necessarily distinct) primes.

4, 6, 12, 18, 28, 30, 42, 44, 46, 49, 51, 55, 60, 62, 65, 69, 72, 74, 77, 80, 82, 91, 98, 99, 100, 102, 104, 106, 108, 111, 115, 125, 126, 129, 136, 138, 148, 150, 152, 153, 155, 161, 164, 166, 169, 171, 172, 174, 175, 180, 183, 185, 187, 189, 190, 192, 194, 196

Offset: 1

Author

Giovanni Teofilatto, Aug 20 2005

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A109287, A109288, A109289.

Programs

Maple

filter:= proc(n)
   if n::even then numtheory:-bigomega(n+1) <> 2 and numtheory:-bigomega(n-1) <> 2
   elif n mod 4 = 1 then not isprime(n) and not isprime((n+1)/2)
   else not isprime(n) and not isprime((n-1)/2)
   fi
end proc:
select(filter, [$4..200]); # Robert Israel, Apr 20 2021

Mathematica

bo[n_] := Plus @@ Last /@ FactorInteger[n]; Select[Range[2, 200], ! (PrimeQ[ # ] || bo[ # - 1] == 2 || bo[ # + 1] == 2) &] (* Ray Chandler, Aug 27 2005 *)

Extensions

Corrected and extended by Ray Chandler, Aug 27 2005