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%I #18 May 21 2017 18:28:37
%S 6,30,42,60,66,70,78,84,90,110,114,120,126,150,174,186,190,204,210,
%T 246,290,294,300,322,330,336,385,390,414,420,450,462,510,540,546,570,
%U 630,660,690,714,720,770,780,786,798,840,846,858,870,910
%N Numbers n with omega(n) > omega of 3 nearest larger and 3 nearest smaller neighbors.
%H G. C. Greubel, <a href="/A101939/b101939.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t 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++]
%t 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 *)
%t Select[Range[650], PrimeNu[#] > Max[PrimeNu[# - 1], PrimeNu[# - 2], PrimeNu[# - 3], PrimeNu[# + 1], PrimeNu[# + 2], PrimeNu[# + 3]] &] (* _G. C. Greubel_, May 21 2017 *)
%Y Cf. A001221, A076763, A101937.
%K easy,nonn
%O 1,1
%A _Neil Fernandez_, Dec 21 2004
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