A157483 Numbers k such that k-1 and k+1 are divisible by exactly 3 primes, counted with multiplicity.

19, 29, 43, 51, 67, 69, 77, 115, 171, 173, 187, 189, 237, 243, 245, 267, 274, 283, 285, 291, 317, 344, 355, 386, 403, 405, 411, 424, 427, 429, 435, 437, 476, 507, 597, 603, 604, 605, 638, 653, 664, 669, 723, 763, 776, 787, 789, 846, 891, 893, 907, 926, 963

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Mar 01 2009

Keywords

• nonn

Comments

Omega(a(n) - 1) = Omega(a(n) + 1) = 3, where Omega(n)=A001222(n). In general twin k-almost prime pairs are defined by Omega(a(n) - 1) = Omega(a(n) + 1) = k. Twin 1-almost primes are twin prime pairs (A014574). - Redjan Shabani, Jul 20 2012

Examples

			19 is a term: 19-1 = 18 = 2*3*3 and 19+1 = 20 = 2*2*5.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A124936, A014612, A156028.

Programs

Maple

with(numtheory); a := proc (n) if bigomega(n-1) = 3 and bigomega(n+1) = 3 then n else end if end proc: seq(a(n), n = 2 .. 1100); # Emeric Deutsch, Mar 03 2009

Mathematica

q=3;lst={};Do[If[Plus@@Last/@FactorInteger[n-1]==q&&Plus@@Last/@FactorInteger[n+1]==q,AppendTo[lst,n]],{n,7!}];lst
Mean/@SequencePosition[PrimeOmega[Range[1000]],{3,,3}] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, Mar 21 2020 *)

PARI

is(n)=bigomega(n-1)==3 && bigomega(n+1)==3 \\ Charles R Greathouse IV, Feb 05 2017

Extensions

More terms from Emeric Deutsch, Mar 03 2009