A101940 Numbers n with omega(n) < omega of 3 nearest larger and 3 nearest smaller neighbors.
37, 53, 89, 97, 113, 121, 157, 163, 173, 211, 223, 233, 251, 263, 277, 289, 293, 307, 317, 331, 337, 343, 353, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 529, 541, 547, 557, 563, 577, 587
Offset: 1
Examples
37 is in the sequence because it has one unique prime factor (itself), whereas 34, 35, 36, 38, 39 and 40 each have more.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
For[i=1, 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++ ] Select[Range[6500], PrimeNu[#] < Min[PrimeNu[# - 1], PrimeNu[# - 2], PrimeNu[# - 3], PrimeNu[# + 1], PrimeNu[# + 2], PrimeNu[# + 3]] &] (* G. C. Greubel, May 21 2017 *)