A101939 Numbers n with omega(n) > omega of 3 nearest larger and 3 nearest smaller neighbors.

6, 30, 42, 60, 66, 70, 78, 84, 90, 110, 114, 120, 126, 150, 174, 186, 190, 204, 210, 246, 290, 294, 300, 322, 330, 336, 385, 390, 414, 420, 450, 462, 510, 540, 546, 570, 630, 660, 690, 714, 720, 770, 780, 786, 798, 840, 846, 858, 870, 910

Offset: 1

Author

Neil Fernandez, Dec 21 2004

Keywords

• easy
• nonn

Examples

			6 is in the sequence because it has two unique prime factors (2 and 3) whereas 3, 4, 5, 7, 8 and 9 each have fewer.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001221, A076763, A101937.

Programs

Mathematica

For[i=3, i<1000, If[And[Length[FactorInteger[i-3]] < Length[FactorInteger[i]], Length[FactorInteger[i-2]] < Length[FactorInteger[i]], Length[FactorInteger[i-1]] < Length[FactorInteger[i]], Length[FactorInteger[i+1]] < Length[FactorInteger[i]], Length[FactorInteger[i+2]] < Length[FactorInteger[i]], Length[FactorInteger[i+3]] < Length[FactorInteger[i]]], Print[i]]; i++]
Clear[noQ];noQ[n_]:=And@@(#?noQ]]+ 3 (* _Harvey P. Dale, Mar 05 2012 *)
Select[Range[650], PrimeNu[#] > Max[PrimeNu[# - 1], PrimeNu[# - 2], PrimeNu[# - 3], PrimeNu[# + 1], PrimeNu[# + 2], PrimeNu[# + 3]] &] (* G. C. Greubel, May 21 2017 *)