A168626 Numbers n such that n and n+-1 have 3 or more distinct prime factors.

645, 741, 805, 987, 1035, 1065, 1105, 1221, 1275, 1309, 1310, 1463, 1495, 1581, 1749, 1885, 1886, 1925, 1989, 2014, 2015, 2109, 2135, 2211, 2255, 2261, 2289, 2295, 2331, 2355, 2365, 2379, 2409, 2465, 2485, 2541, 2584, 2585, 2665, 2666, 2667, 2679, 2685

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Dec 01 2009

Keywords

• nonn

Crossrefs

Subsequence of A321503 and hence of A000977.

Cf. A140077

Programs

Mathematica

f[n_]:=Length[FactorInteger[n]]; lst={};Do[If[f[n]>=3&&f[n-1]>=3&&f[n+1]>=3,AppendTo[lst,n]],{n,7!}];lst
Mean/@SequencePosition[Table[If[PrimeNu[n]>2,1,0],{n,2700}],{1,1,1}] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Jun 05 2016 *)

PARI

is(n)=omega(n)>2 && omega(n-1)>2 && omega(n+1)>2 \\ Charles R Greathouse IV, Jan 25 2025

Formula

a(n) ~ n. - Charles R Greathouse IV, Jan 25 2025

Extensions

Definition clarified by Harvey P. Dale, Jun 05 2016