A136155 Composites one larger than a prime and with exactly two or three distinct prime factors.

6, 12, 14, 18, 20, 24, 30, 38, 42, 44, 48, 54, 60, 62, 68, 72, 74, 80, 84, 90, 98, 102, 104, 108, 110, 114, 132, 138, 140, 150, 152, 158, 164, 168, 174, 180, 182, 192, 194, 198, 200, 212, 224, 228, 230, 234, 240, 242, 252, 258, 264, 270, 272, 278, 282, 284, 294

Offset: 1

Author

Enoch Haga, Dec 16 2007

Keywords

• easy
• nonn

Examples

			a(1)=6, which is one larger than the prime 5 and has 2 distinct prime factors (namely 2 and 3).
60 is in the sequence because 59 is prime and 60 = 2^2*3*5 has three distinct prime factors.
		

Links

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

Crossrefs

Cf. A136151, A136152, A136153, A136154.

Programs

Maple

A001221 := proc(n) nops(numtheory[factorset](n)) ; end: isA136155 := proc(n) if isprime(n-1) then RETURN( A001221(n)=2 or A001221(n)= 3) ; else RETURN(false) ; fi ; end: for n from 1 to 300 do if isA136155(n) then printf("%d,",n) ; fi ; od: # R. J. Mathar, May 03 2008

Mathematica

okQ[n_] := PrimeQ[n-1] && (PrimeNu[n]==2 || PrimeNu[n]==3);
Select[Range[6, 300, 2], okQ] (* Jean-François Alcover, Feb 04 2023 *)

Formula

Union of A136151 and A136152. Subset of A008864. - R. J. Mathar, Apr 24 2008

A136151 UNION A136152. - R. J. Mathar, May 03 2008

Extensions

Edited by R. J. Mathar and Jens Kruse Andersen, Apr 24 2008