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

1,1

Links

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

Example

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.

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@@(#<Max[n]&/@Drop[n, {4}]); Off[Drop::normal]; Off[ Drop::seqs]; Flatten[Position[Partition[ PrimeNu[Range[1000]], 7, 1], _?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 *)

Crossrefs

Cf. A001221, A076763, A101937.

Sequence in context: A336216 A309312 A101937 * A290466 A293188 A080289

Adjacent sequences: A101936 A101937 A101938 * A101940 A101941 A101942

Keyword

easy,nonn

Author

Neil Fernandez, Dec 21 2004

Status

approved